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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 Baum-Connes conjecture, \(E_0\) semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Titles in this series are co-published 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 — Cut-down 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 Baum-Connes 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 quasi-free 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
-
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
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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 Baum-Connes conjecture, \(E_0\) semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Titles in this series are co-published 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 — Cut-down 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 Baum-Connes 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 quasi-free 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
