CONTEMPORARY MATHEMATICS

228

Operator Algebras and Operator Theory

International Conference on Operator Algebras and Operator Theory

July 4-9, 1997 Shanghai, China

Liming Ge Huaxin Lin

Zhong-Jin Ruan Dianzhou Zhang Shuang Zhang

Editors

Selected Titles in This Series

228 Liming Ge, Huaxin Lin, Zhong-Jin Ruan, Dianzhou Zhang, and Shuang Zhang, Editors, Operator algebras and operator theory, 1998

227 John McCleary, Editor, Higher homotopy structures in topology and mathematical physics, 1999

226 Luis A. Caffarelli and Mario Milman, Editors, Monge Ampere equation: Applications to geometry and optimization, 1999

225 Ronald C. Mullin and Gary L. Mullen, Editors, Finite fields: Theory, applications, and algorithms, 1999

224 Sang Geun Hahn, Hyo Chul Myung, and Efim Zelmanov, Editors, Recent progress in algebra, 1999

223 Bernard Chazelle, Jacob E. Goodman, and Richard Pollack, Editors, Advances in discrete and computational geometry, 1999

222 Kang-Tae Kim and Steven G. Krantz, Editors, Complex geometric analysis in Pohang, 1999

221 J. Robert Dorroh, Gisele Ruiz Goldstein, Jerome A. Goldstein, and Michael Mudi Tom, Editors, Applied analysis, 1999

220 Mark Mahowald and Stewart Priddy, Editors, Homotopy theory via algebraic geometry and group representations, 1998

219 Marc Henneaux, Joseph Krasil'shchik, and Alexandre Vinogradov, Editors, Secondary calculus and cohomological physics, 1998

218 Jan Mandel, Charbel Farhat, and Xiao-Chuan Cai, Editors, Domain decomposition methods 10, 1998

217 Eric Carlen, Evans M. Harrell, and Michael Loss, Editors, Advances in differential equations and mathematical physics, 1998

216 Akram Aldroubi and EnBing Lin, Editors, Wavelets, multiwavelets, and their applications, 1998

215 M. G. Nerurkar, D. P. Dokken, and D. B. Ellis, Editors, Topological dynamics and applications, 1998

214 Lewis A. Coburn and Marc A. Rieffel, Editors, Perspectives on quantization, 1998 213 Farhad Jafari, Barbara D. MacCluer, Carl C. Cowen, and A. Duane Porter,

Editors, Studies on composition operators, 1998 212 E. Ramirez de Arellano, N. Salinas, M. V. Shapiro, and N. L. Vasilevski,

Editors, Operator theory for complex and hypercomplex analysis, 1998 211 Jozef Dodziuk and Linda Keen, Editors, Lipa's legacy: Proceedings from the Bers

Colloquium, 1997 210 V. Kumar Murty and Michel Waldschmidt, Editors, Number theory, 1998 209 Steven Cox and Irena Lasiecka, Editors, Optimization methods in partial differential

equations, 1997 208 MichelL. Lapidus, Lawrence H. Harper, and Adolfo J. Rumbos, Editors,

Harmonic analysis and nonlinear differential equations: A volume in honor of Victor L. Shapiro, 1997

207 Yujiro Kawamata and Vyacheslav V. Shokurov, Editors, Birational algebraic geometry: A conference on algebraic geometry in memory of Wei-Liang Chow (1911-1995), 1997

206 Adam Koranyi, Editor, Harmonic functions on trees and buildings, 1997 205 Paulo D. Cordaro and Howard Jacobowitz, Editors, Multidimensional complex

analysis and partial differential equations: A collection of papers in honor of Fran<;ois Treves, 1997

204 Yair Censor and Simeon Reich, Editors, Recent developments in optimization theory and nonlinear analysis, 1997

(Continued in the back of this publication)

http://dx.doi.org/10.1090/conm/228

Operator Algebras and Operator Theory

CoNTEMPORARY MATHEMATICS

228

Operator Algebras and Operator Theory

International Conference on Operator Algebras and Operator Theory

July 4-9, 1997 Shanghai, China

Liming Ge Huaxin Lin

Zhong-Jin Ruan Dianzhou Zhang Shuang Zhang

Editors

American Mathematical Society Providence, Rhode Island

Editorial Board

Dennis DeTurck, managing editor

Andreas Blass Andy R. Magid Michael Vogelius

This volume contains proceedings of the 1997 International Conference on Operator Algebras and Operator Theory, held at East China University, Shanghai, China on July 4-9, 1997.

1991 Mathematics Subject Classification. Primary 47 A05, 47D15, 46L05, 46L10, 46L80.

Library of Congress Cataloging-in-Publication Data International Conference on Operator Algebras and Operator Theory ( 1997 : Shanghai, China)

Operator algebras and operator theory : International Conference on Operator Algebras and Operator Theory, July 4-9, 1997, Shanghai, China / Liming Ge ... [et al.], editors.

p. em. - (Contemporary mathematics ; 228) Includes bibliographical references. ISBN 0-8218-1093-6 (alk. paper) 1. Operator algebras--Congresses. 2. Operator theory-Congresses. I. Ge, Liming, 1965

II. Title. III. Series: Contemporary mathematics (American Mathematical Society) ; v. 228. QA326.I57 1997 512'.55-dc21 98-41143

CIP

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10 9 8 7 6 5 4 3 2 1 03 02 01 00 99 98

Contents

Preface 1x

Foreword x1

List of Participants xm

Program xvii

Operator means and spectral decomposability in ergodic theory and Hilbert space operator theory EARL BERKSON AND T. A. GILLESPIE 1

Some remarks on Toeplitz operators on discrete groups XIAOMAN CHEN AND QINGXIANG Xu 17

A general construction of bivariant K-theories on the category of C* -algebras JOACHIM CUNTZ 31

Residually finite dimensional C* -algebras MARIUS DADARLAT 45

O.Cp spaces EDWARD G. EFFROS AND ZHONG-JIN RUAN 51

Simple inductive limits of C* -algebras with building blocks from spheres of odd dimension GEORGE A. ELLIOTT AND XIAOCHUN FANG 79

Approximate divisibility of simple inductive limit C* -algebras GEORGE A. ELLIOTT, GUIHUA GONG, AND LIANGQING LI 87

On maximality of entropy in finite von Neumann algebras UFFE HAAGERUP AND ERLING ST0RMER 99

Free entropy and approximate equivalence in von Neumann algebras DoN HADWIN 111

Bivariant Chern character and the analog Baum-Connes map RONGHUI Ji 133

Dual cones and Tomita-Takesaki theory RICHARD V. KADISON 151

vii

viii ( 'ONTENTS

Subfactors and paragroup theory YASGYUKI KAWAHIGASHI 179

Notes on C* -algebras of graphs A. KuMJIAN 189

Frames and wavelets from an operator theoretic point of view DAVID R LARSON 201

A classification theorem for infinite Toeplitz algebras HUAXIN LIN 219

AH algebras with the ideal property CORNEL PASNICU 277

Ordered K-theory for C* -algebras of minimal homeomorphisms Q. LIN AND N. CHRISTOPHER PHILLIPS 289

Questions on quantization MARC A. RIEFFEL 315

On sums of finite projections MIKAEL R0RDAM 327

Groupoid approach to quantum projective spaces ALBERT JEU-LIANG SHEC 341

Representations of topological dynamical systems and C* -algebras JUN TOMIYAMA 351

Purely infinite simple C* -algebras arising from reduced group C* -algebras SHUANG ZHANG 365

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X PREFACE

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Foreword

During recent years, many important achievements have been made in operator algebras, operator theory and related areas. In 1996, a group of mathematicians working in related areas decided to hold an international conference on operator algebras and operator theory in one of the cradles of ancient mathematics-China. We had the privilege to organize the International Conference on Operator Algebras and Operator Theory at the East China Normal University in Shanghai, China from July 4 to July 9, 1997.

More than 120 people participated in this conference, ranging from graduate students and postdoctors to the leading experts. Among the participants, seventy-five people came from Canada, Denmark, France, Germany, Italy, Israel, Japan, Norway, Poland, Russia, Sweden and USA and the rest came from Taiwan, Hong Kong, and various centers in the mainland of China. There were fifteen main speakers, six other plenary speakers and thirty-five speakers in parallel sessions. The conference topics were C* -algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces, and other related areas. The confer-ence was extremely successful.

This volume consists mainly of contributions from some invited speakers and a few other mathematicians who could not attend the conference. We wish that this volume of conference proceedings will not only communicate important mathemat-ical ideas but also record this unique, exciting event.

We take this opportunity to thank the National Natural Science Foundation of China and the National Science Foundation of the United States for their generous financial support. We also wish to thank the East China Normal University for their warm hospitality, and expecially to thank the faculties and graduate students from the mathematics department who provided the extremely valuable help. Finally, we would like to acknowledge the following individuals who deserve our special appreciation for their support of the meeting and the publication of the volume: Sanwen Hu, Jiyian Wang, J. Tomiyama, and G. A. Elliott.

Liming Ge Huaxin Lin Zhong-Jin Ruan Dianzhou Zhang Shuang Zhang

(Note: This is not the translation from the Chinese preface.)

xi

William Arveson Earl Berkson Bruce Blackadar Ola Bratteli Xiaohong Cao Man-Duen Choi Xiaoman Chen Erik Christensen Jianlian Cui J oachem Cuntz Xinde Dai Hongke Du George Elliott Edward Effros Xiaochun Fang Carla Farsi Sarah Ferguson Masatoshi Fujii Igor Fulman Takayuki Furuta Mingwu Gao Liming Ge Guihua Gong Ming Gong Kunyu Guo Caixing Gu Don Hadwin Xiaojie Hong Jeong-Hee Hong Thomas Hoover Chengjun Hou Jinchuan Hou Shengzhao Hou Junyun Hu Shanwen Hu Danrun Huang Takashi Itoh Ja A Jeong

List of Participants

xiii

Berkeley, USA Urbana-Champaign, USA Reno, USA Oslo, Norway Qufu, China Toronto, Canada Shanghai, China Copenhagen, Denmark Linfen, China Heideberg, Germany Hanzhou, China Xi'an, China Toronto, Canada Los Angeles, USA Shanghai, China Boulder, USA W. Lafaytte, USA Osaka, Japan Iowa, City, USA Tokyo, Japan Linfen, China Cambridge, USA Puerto, Rico, USA Hangzhou, China Shanghai, China California, USA Durham, USA Shanghai, China Pusan, Korea Honolulu, USA Qufu, China Linfen, China Linfen, China Shanghai, China Shanghai, China Seattle, USA Gunma, Japan Seoul, Korea

xiv

Ronghui Ji Peisheng Ji Guangjie Jiang Eizaburo Kamei Yasuyuki Kawahigashi Alexander Kumjian Seung-Hyeok Kye Alan Lambert David Laarson SaGe Lee Bingren Li Liangqing Li Minli Li Shaokuan Li Zhongyan Li Huaxin Lin Junping Liu Yufeng Lu Shijie Lu Jianwen Luo Vladimir Manuilov K. Matsumoto Jesper Mygind Yoshiomi N akagami Chi-Keung Ng Hiroyuki Osaka Chun-Gil Park Cornel Pasnicu Hemant Pendharkar N. Christopher Phillips Gilles Pisier

Marc Rieffel Mikael Rordam Zhong-jin Ruan Oyvind Ryan S. L. Saavedra Norberto Salinas A. Jeu-Liang Sheu Sergei Silvestrov Baruch Solel Erlings Stormer Takahiro Sudo F. H. Szafraniec Ping K warn Tam Masamichi Takesaki Klaus Thomsen Jun Tomiyama

LIST OF PARTICIPANTS

Indianapolis, USA Jinan, China Xi'an, China Gunma, Japan Tokyo, Japan Reno, USA Seoul, Korea Charlotte, USA College Station, USA Seoul, Korea Beijing, China Puerto Rico, USA Beijing, China Shanghai, China Qufu, China Engene, USA Shanghai, China Changchun, China Hangzhou, China Hangzhou, China Moscow, Russia Joetsu, Japan Aarhus, Denmark Yokohama, Japna Oxford, UK Okinaua, Japan Taejon, Korea San Juan, USA Durham, USA Eugene, USA Paris, France and

College Station, USA Berkeley, USA Odense, Denmark Urbana-Champaign, USA Oslo, NOrway Sevilla, Spain Lawrence, USA Lawrence, USA Stockholm, Sweden Haifa, Israel Oslo, Norway Tokyo, Japan Krakow, Poland Hong Kong, China Los Angeles, USA Aarhus, Denmark Tokyo, Japan

Liguang Wang Qin Wang Yongge Wang Yuejian Wang Zongyao Wang Yasuo Watatani Nik Weaver Changguo Wei Gongming Wei Guo Qiang Wei Shuyun Wei Gary Weiss Carl Winslow Ngai-Ching Wong Baowei Wu Liangsen Wu Ho'an Xie Benlong Xu Shengzhi Xu Tianzhou Xu Shigeru Y amagami Yamazami Yamagida Guoliang Yu Jeffery R. Zak Liuchuan Zeng Dianzhou Zhang Shuang Zhang Xiaofei Zhang Xiaoxia Zhang Nina Zorboska

LIST OF PARTICIPANTS

Shanghai, China Shanghai, China Qufu, China Changehun, China Shanghai, China Fukuoka, Japan Los Angeles, USA Shanghai, China Shanghai, China Shanghai, China Shanghai, China Cincinnnati, USA Copenhagen, Denmark Kaohsiung, Taiwan Xi'an, China Shanghai, China Shanghai, China Qufu, Chain Shanghai, China Beijing, China Sendai, Japan Tokyo, Japan Tokyo, Japan Boulder, USA Dover, USA Shanghai, China Shanghai, China Cubcubbatum YSA Hnhzhou, China Qufu, China Winnipeg, Canada

XV

Program

Friday, July 4 Morning Session

Chairman: D. Zhang 8:00-8:25 Opening and the address of the president of the East China Norma

University Chairman: H. Lin

8:30-9:20 G. Elliott: The structure and classification problem from amenabl1 C* -algebras.

Chairman: L. Ge 9:50-10:40 M. Rieffel: Proper actions of groups on C* -algebras.

10:45-11:35 D. Larson: Frames, wavelets and group presentations. 11:40-12:05 L. Wu: Positive definite generalized functions.

Afternoon Session Session A

Chairman: : Z-J Ruan 14:00-14:30 X. Dai: An operator-theoritic technique in wavelet theory. 14:35-15:05 R. Ji: Bivariant Chern character of Baum-Connes map. 15:10-15:40 A. Kumjian: C* -algebras of directed graphs and group action. 16:10-16:40 E. Christensen: lnvetibility preserving. 16:45-17:15 D. Huang: Flow equivalence and Cuntz-Kreiger algebras. Session B

Chairman: S. Zhang 14:00-14:30 T. Furuta: Operator inequality. 14:35-15:05 K. Thomsen: E-theory and C* -extension. 15:10-15:40 S. Yamagami: Amenability of commutative Fusion. 16:10-16:40 S. Ferguson: Derivation of the polydisk algebra. 16:45-17:15 D. Hadwin: Approximate equivalenceand free entropy.

Saturday, July 5 Morning Session

Chairman: Z-J Ruan 8:00-8:50 E. Effros: The predual of a von Neumann algebra is locally reflexive. 8:55-9:45 E. Berkson: Quadratic operator means and spectral decomposability.

xvii

xviii PROGRAM

Chairman: S. Zhang 9:55-10:45 M-D Choi: Almost commuting unitaries.

10:50-11:15 G. Gong: On the classification of simple C* -algebras. 11:20-11:45 B. Blackadar: Generalized inductive limits of finite-dimensional C* -algebra 11:50-12:15 0. Bratteli: Representations of Cuntz algebras coming from wavelets.

Afternoon

Social Events and City Tour

Sunday, July 6 Morning Session

Chairman: Z-J Ruan 8:00-8:50 G. Pisier: The similarity degree of an operator algebra. 9:00-9:50 M. Takesaki: The characteristic square for factors and cocycle conjugacy <

discrete amenable group actions on AFD factors. Chairman: J. Tomiyama

10:10-11:00 Y. Kawahigashi: Equivalent subfactors and quantum Galois correspondenc• 11:05-11:30 Y. Watatani: Jones index theory and Hilbert C*-bimodule. 11:35-12:00 M. Rordam: On stable C*-algebras.

Afternoon Session Session A

Chairman: J. Hou 14:00-14:20 E. Kamei: Monotone properties of operator functions associated with Furut

inequality. 14:25-14:45 F. Szafraniec: Unbounded subnormal operators. 14:50-15:10 Y. Lu: Local decomposition of essential spectra of Toeplitz operators o

H(S). 15:15-15:35 M. Gao: Local C-semigroups and C-cosine operator functions.

Chairman: S. Li 16:00-16:20 J. Hou: Miltiplicative maps on B(H). 16:25-16:45 J. Hong: Composition of subfactors and twisted bicrossed products. 16:50-17:10 Y. Wang: Commutant and reducing subspaces of certain analytic Toeplit

operators on the Bergman spaces. 17:15-17:35 I. Fulman: Fell bundles over equivalence relations. Session B

Chairman: C. Gu 14:00-14:20 N. Weaver: Noncomutative complex analysis. 14:25-14:45 V. Manuilov: Asymtotic group representations. 14:50-15:10 J. Jeong: Cancellation of C* -crossed products. 15:15-15:35 X. Fang: About the multiplier of Hilbert module.

Chairman: A. Sheu 16:00-16:20 C. Ng: Duality of Hop£ C* -algebras. 16:25-16:45 S. Silverstrov: A bounded and unbounded representations of a q-deforme<

Lie algebra and dynamical system. 17:15-17:35 C. Gu: Casual commutant lifting theory and nonlinear robust control. Session C

Chairman: H. Du 14:00-14:20 N-C Wong: A supplement to result of Shultz and Brown.

PROGRAM

14:25-14:45 S. Saavedra: Hipercyclic operators. 14:50-15:10 B. Solel: Operator algebras associated with C*-correspondences. 15:15-15:35 S. Lu: Isomorphisms on triangular algebras.

Chairman: S. Lu

xix

16:00-16:20 C. Park: The homotopy groups of the automorphism groups of non- com-mutative tori.

16:25-16:45 T. Sudo: Dimenion theory of C*-algebras of Lie groups. 16:50-17:10 H. Du: (title unavailable) 17:15-17:35 S. Lee: About C*-algebras and von Neumann algebras.

Monday, 7 Suzhou Tour famous Shanghai

Tuesday, July 8

Chairman: M-D Choi Morning Session

8:00-8:50 J. Cuntz: Bivariant K-theory for locally convex algebras and the Chern-Connes character.

9:00-9:50 W. Arveson: The energy sequence of an operator space. Chairman: R. Ji

10:10-11:00 N. Salinas: The gauge invariant Toeplitz algebra on the Hardy space over SL(2, R).

11:05-11:30 C. Phillips: Subhomogeneous approximation of minimal smooth dynamical systems.

11:35-12:00 X. Chen: Toeplitz operators and extensions on Hilbert C* -modules.

Afternoon Session Session A

Chairman: Y. Kawahigashi 14:00-14:30 A. Sheu: Groupoid approach to quantum groups. 14:35-15:05 T. Itoh: Grothendieck type norms for bilinear forms on C* -algebras. 15:10-15:40 C. Pasnicu: AH-algebras with the ideal property. 15:55-16:25 K. Matsumoto: Symbolic dynamics and C* -algebras. 16:30-17:00 C. Winslow: Topology in the space of von Neumann algebras. Session B Chairman: G. Gong 14:00-14:30 C. Farsi: (Soft) Rotation algebras, non-commutative tori and operator iden-

tities. 14:35-15:05 H. Osaka: Extremal richness of C* -algebras. 15:10-15:40 S. Kye: On the convex cone of all positive linear maps in matrix algebras. 15:55-16:25 G. Yu: The Novikov conjecture. 16:30-17:00 A. Lambert: Conditional independence and Hilbert C* -modules.

Wednesday, July 9 Morning Session

Chairman: L. Ge 8:00-8:50 B. Li: Real operator algebras. 8:55-9:45 E. Stormer: Maximality of entropy in finte von Neumann algebras.

XX PROGRAJ\I

Chairman: M. Takesaki 10:05-10:55 Y. Nakagami: Operator algebras for compact Hopf *-algberas. 11:00-11:25 G. Weiss: The commutator structure of operator ideals.

Selected Titles in This Series (Continued from the front of this publication)

203 Hanna Nencka and Jean-Pierre Bourguignon, Editors, Geometry and nature: In memory of W. K. Clifford, 1997

202 Jean-Louis Loday, James D. Stasheff, and Alexander A. Voronov, Editors, Operads: Proceedings of Renaissance Conferences, 1997

201 J. R. Quine and Peter Sarnak, Editors, Extremal Riemann surfaces, 1997 200 F. Dias, J.-M. Ghidaglia, and J.-C. Saut, Editors, Mathematical problems in the

theory of water waves, 1996 199 G. Banaszak, W. Gajda, and P. Krason, Editors, Algebraic K-theory, 1996 198 Donald G. Saari and Zhihong Xia, Editors, Hamiltonian dynamics and celestial

mechanics, 1996 197 J. E. Bonin, J. G. Oxley, and B. Servatius, Editors, Matroid theory, 1996 196 David Bao, Shiing-shen Chern, and Zhongmin Shen, Editors, Finsler geometry,

1996 195 Warren Dicks and Enric Ventura, The group fixed by a family of injective

endomorphisms of a free group, 1996 194 Seok-Jin Kang, Myung-Hwan Kim, and Insok Lee, Editors, Lie algebras and their

representations, 1996 193 Chongying Dong and Geoffrey Mason, Editors, Moonshine, the Monster, and

related topics, 1996 192 Tomek Bartoszynski and Marion Scheepers, Editors, Set theory, 1995 191 Tuong Ton-That, Kenneth I. Gross, Donald St. P. Richards, and Paul J. Sally,

Jr., Editors, Representation theory and harmonic analysis, 1995 190 Mourad E. H. Ismail, M. Zuhair Nashed, Ahmed I. Zayed, and Ahmed F.

Ghaleb, Editors, Mathematical analysis, wavelets, and signal processing, 1995 189 S. A.M. Marcantognini, G. A. Mendoza, M.D. Moran, A. Octavio, and W. 0.

Urbina, Editors, Harmonic analysis and operator theory, 1995 188 Alejandro Adem, R. James Milgram, and Douglas C. Ravenel, Editors,

Homotopy theory and its applications, 1995 187 G. W. Brumfiel and H. M. Hilden, SL(2) representations of finitely presented groups,

1995 186 Shreeram S. Abhyankar, Walter Feit, Michael D. Fried, Yasutaka Ihara,

and Helmut Voelklein, Editors, Recent developments in the inverse Galois problem, 1995

185 Raul E. Curto, Ronald G. Douglas, Joel D. Pincus, and Norberto Salinas, Editors, Multivariable operator theory, 1995

184 L. A. Bokut', A. I. Kostrikin, and S. S. Kutateladze, Editors, Second International Conference on Algebra, 1995

183 William C. Connett, Marc-Olivier Gebuhrer, and Alan L. Schwartz, Editors, Applications of hypergroups and related measure algebras, 1995

182 Selman Akbulut, Editor, Real algebraic geometry and topology, 1995 181 Mila Cenkl and Haynes Miller, Editors, The Cech Centennial, 1995 180 David E. Keyes and Jinchao Xu, Editors, Domain decomposition methods in

scientific and engineering computing, 1994 179 Yoshiaki Maeda, Hideki Omoro, and Alan Weinstein, Editors, Symplectic

geometry and quantization, 1994 178 Helene Barcelo and Gil Kalai, Editors, Jerusalem Combinatorics '93, 1994 177 Simon Gindikin, Roe Goodman, Frederick P. Greenleaf, and Paul J. Sally, Jr.,

Editors, Representation theory and analysis on homogeneous spaces, 1994 176 David Ballard, Foundational aspects of "non"standard mathematics, 1994

(See the AMS catalog for earlier titles)

ISBN D-8218-1 093-6

9 780821 810934