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Book DetailsFields Institute CommunicationsVolume: 13; 1997; 323 ppMSC: Primary 46;
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas—both within and outside mathematics. The field was a natural candidate for a 1994–1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences.
This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable \(C^*\)algebras, the BaumConnes conjecture, \(E_0\) semigroups, subfactors, Etheory, quasicrystals, and the solution to a longstanding problem in operator theory: Can almost commuting selfadjoint matrices be approximated by commuting selfadjoint matrices?
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students, research mathematicians, and physicists interested in functional analysis.

Table of Contents

Chapters

William Arveson — Minimal $E_0$semigroups

Dietmar Bisch — Bimodules, higher relative commutants, and the fusion algebra associated to a subfactor

David Blecher — On selfdual Hilbert modules

Soren Eilers — Künneth splittings and classification of $C^*$algebras with finitely many ideals

George Elliott and Qing Lin — Cutdown method in the inductive limit decomposition of noncommutative tori. II: The degenerate case

George Elliott, Guihua Gong, Xinhui Jiang and Hongbing Su — A classification of simple limits of dimension drop $C^*$algebras

Pierre Julg — Remarks on the BaumConnes conjecture and Kazhdan’s property $T$

Johannes Kellendonk — Integer groups of coinvariants associated to octagonal tilings

Eberhard Kirchberg — On the existence of traces on exact stably projectionless simple $C^*$algebras

Akitaka Kishimoto and Alexander Kumjian — Crossed products of Cuntz algebras by quasifree automorphisms

Huaxin Lin — Almost commuting selfadjoint matrices and applications

Huaxin Lin and Hiroyuki Osaka — Real rank of multiplier algebras of $C^*$lgebras of real rank zero

N. Phillips — Approximate unitary equivalence of homomorphisms from odd Cuntz algebras

Mikael Rordam — Classification of certain infinite simple $C^*$algebras. III

Shoichiro Sakai — KMS states and phase transitions. II

Jonathan Samuel — Asymnptotic morphisms and $E$theory

Klaus Thomsen — Representing $K_1$ in the unitary group


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The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas—both within and outside mathematics. The field was a natural candidate for a 1994–1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences.
This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable \(C^*\)algebras, the BaumConnes conjecture, \(E_0\) semigroups, subfactors, Etheory, quasicrystals, and the solution to a longstanding problem in operator theory: Can almost commuting selfadjoint matrices be approximated by commuting selfadjoint matrices?
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students, research mathematicians, and physicists interested in functional analysis.

Chapters

William Arveson — Minimal $E_0$semigroups

Dietmar Bisch — Bimodules, higher relative commutants, and the fusion algebra associated to a subfactor

David Blecher — On selfdual Hilbert modules

Soren Eilers — Künneth splittings and classification of $C^*$algebras with finitely many ideals

George Elliott and Qing Lin — Cutdown method in the inductive limit decomposition of noncommutative tori. II: The degenerate case

George Elliott, Guihua Gong, Xinhui Jiang and Hongbing Su — A classification of simple limits of dimension drop $C^*$algebras

Pierre Julg — Remarks on the BaumConnes conjecture and Kazhdan’s property $T$

Johannes Kellendonk — Integer groups of coinvariants associated to octagonal tilings

Eberhard Kirchberg — On the existence of traces on exact stably projectionless simple $C^*$algebras

Akitaka Kishimoto and Alexander Kumjian — Crossed products of Cuntz algebras by quasifree automorphisms

Huaxin Lin — Almost commuting selfadjoint matrices and applications

Huaxin Lin and Hiroyuki Osaka — Real rank of multiplier algebras of $C^*$lgebras of real rank zero

N. Phillips — Approximate unitary equivalence of homomorphisms from odd Cuntz algebras

Mikael Rordam — Classification of certain infinite simple $C^*$algebras. III

Shoichiro Sakai — KMS states and phase transitions. II

Jonathan Samuel — Asymnptotic morphisms and $E$theory

Klaus Thomsen — Representing $K_1$ in the unitary group