This volume reflects the proceedings of the U.S.-Japan seminar on Operator Algebras and Applications held at Kyushu University (Japan). Contributors to the volume are leading researchers in the theory of operator algebras.

Readers will find a variety of current research topics reflecting the state of the art of the subject. Topics covered include the classification of $C^*$-algebras by $K$-theoretical data and related topics, a detailed study on various classes of $C^*$-algebras, subfactor analysis and related topics, free probability theory, and more. The material is suitable for graduate students and researchers interested in operator algebras and their applications.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and research mathematicians interested in operator algebras and their applications.

Table of Contents

• B. Blackadar -- Semiprojectivity in simple $C^*$-algebras
• N. Brown -- On quasidiagonal $C^*$-algebras
• N. Brown and M. Dadarlat -- Extensions of quasidiagonal $C^*$-algebras and $K$-theory
• J. H. Hong -- The ideal structure of graph algebras
• J. A. Jeong -- Stable rank and real rank of graph $C^*$-algebras
• Q. Lin and N. C. Phillips -- Direct limit decompostion for $C^*$-algebras of minimal diffeomorphisms
• M. Nagisa -- Single generation and rank of $C^*$-algebras
• H. Nakamura -- Aperiodic automorphisms of certain simple $C^*$-algebras
• C.-G. Park -- $C^*$-algebras over sphere with fibres non-commutative tori
• M. Rørdam -- Stable $C^*$-algebras

• M. Izumi -- Non-commutative Markov operators arising from subfactors
• Y. Kawahigashi -- Braiding and nets of factors on the circle
• N. Sato -- A notion of Morita equivalence between subfactors
• Y. Ueda -- Amalgamated free product over Cartan subalgebra, II. Supplementary results and examples

• T. Digernes -- Finite approximations and physics over unconventional fields
• F. Hiai and H. Kosaki -- Operator means and their norms
• T. Matsui -- Quantum spin chain and Popescu systems
• K. Matsumoto -- Topological conjugacy invariants of symbolic dynamics arising from $C^*$-algebra $K$-theory
• Y. Watatani -- Relative positions of four subspaces in a Hilbert space and subfactors