Mappings of Operator Algebras

1. Front Matter

   Pages i-x

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2. On Convex Combinations of Unitary Operators in C*-Algebras

   • Uffe Haagerup

   Pages 1-13

3. Approximately Inner Derivations, Decompositions and Vector Fields of Simple C*-Algebras

   • Palle Jorgensen

   Pages 15-113

4. Derivations in Commutative C*-Algebras

   • H. Kurose

   Pages 115-118

5. Representation of Quantum Groups

   • Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, Kimio Ueno

   Pages 119-128

6. Automorphism Groups and Covariant Irreducible Representations

   • Akitaka Kishimoto

   Pages 129-139

7. Proper Actions of Groups on C*-Algebras

   • Marc A. Rieffel

   Pages 141-182

8. On The Baum-Connes Conjecture

   • Hiroshi Takai

   Pages 183-197

9. On Primitive Ideal Spaces of C*-Algebras over Certain Locally Compact Groupoids

   • Shigeru Yamagami

   Pages 199-204

10. On Sequences of Jones’ Projections

    • Marie Choda

    Pages 205-218

11. The Powers’ Binary Shifts on the Hyperfinite Factor of Type II1

    • Masatoshi Enomoto

    Pages 219-225

12. Index Theory for Type III Factors

    • Hideki Kosaki

    Pages 227-231

13. Relative Entropy of a Fixed Point Algebra

    • Satoshi Kawakami

    Pages 233-238

14. Jones Index Theory for C*-Algebras

    • Yasuo Watatani

    Pages 239-250

15. Three Tensor Norms for Operator Spaces

    • Vern I. Paulsen

    Pages 251-264

16. Extension Problems for Maps on Operator Systems

    • R. R. Smith

    Pages 265-273

17. Multivariable Toeplitz Operators and Index Theory

    • Harald Upmeier

    Pages 275-288

18. On Maximality of Analytic Subalgebras Associated with Flow in von Neumann Algebras

    • Kichi-Suke Saito

    Pages 289-293

19. Reflections Relating a von Neumann Algebra and Its Commutant

    • Richard V. Kadison

    Pages 295-304

20. Normal AW*-Algebras

    • Kazuyuki Saitô, J. D. M. Wright

    Pages 305-307

This volume consists of articles contributed by participants at the fourth Ja­ pan-U.S. Joint Seminar on Operator Algebras. The seminar took place at the University of Pennsylvania from May 23 through May 27, 1988 under the auspices of the Mathematics Department. It was sponsored and supported by the Japan Society for the Promotion of Science and the National Science Foundation (USA). This sponsorship and support is acknowledged with gratitude. The seminar was devoted to discussions and lectures on results and prob­ lems concerning mappings of operator algebras (C*-and von Neumann alge­ bras). Among the articles contained in these proceedings, there are papers dealing with actions of groups on C* algebras, completely bounded mappings, index and subfactor theory, and derivations of operator algebras. The seminar was held in honor of the sixtieth birthday of Sh6ichir6 Sakai, one of the great leaders of Functional Analysis for many decades. This vol­ ume is dedicated to Professor Sakai, on the occasion of that birthday, with the respect and admiration of all the contributors and the participants at the seminar. H. Araki Kyoto, Japan R. Kadison Philadelphia, Pennsylvania, USA Contents Preface.... ..... ....... ........... ...... ......... ................ ...... ............... ... vii On Convex Combinations of Unitary Operators in C*-Algebras UFFE HAAGERUP ......................................................................... .

• C*-algebra
• algebra
• automorphism
• functional analysis
• index theory
• operator algebra

• Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

  Huzihiro Araki

• Department of Mathematics, University of Pennsylvania, Philadelphia, USA

  Richard V. Kadison

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