Almost commuting unitaries and classification of purely infinite simple \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Almost commuting unitaries and classification of purely infinite simple \(C^*\)-algebras
zbMATH Open document ID: 0922.46054
author: Huaxin Lin
published in: Journal of Functional Analysis
publication date: 1998-10-27T00:00:00Z
review text: The author proves some results on approximating pairs of almost commuting unitaries by commuting unitaries. These are applied to show, e.g., that \[ {\mathcal A}_\theta\otimes{\mathcal O}_2\cong\ell_2 \quad\text{and}\quad {\mathcal B}_\theta\otimes{\mathcal O}_2\cong{\mathcal O}_2, \] where \({\mathcal A}_\theta\) and \({\mathcal B}_\theta\) are an irrational rotation algebra and a Bunce-Deddens algebra, respectively. These special results originally obtained in 1993 are now superseded by the work of E. Kirchberg and N. C. Philipps (1997).
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 1199743
zbMATH Keywords: almost commuting unitaries
zbMATH Keywords: classification of purely infinite simple \(C^\ast\)-algebras
zbMATH Keywords: irrational rotation algebra
zbMATH Keywords: Bunce-Deddens algebra
MaRDI profile type: Publication
full work available at URL: jfan.1997.3214
OpenAlex ID: W2010420322
cites work: Multipliers of C -algebras
cites work: Almost commuting matrices and a quantitative version of the Brown- Douglas-Fillmore theorem
cites work: Q5287660
cites work: Q4403336
cites work: Extensions of \(C^*\)-algebras and \(K\)-homology
cites work: Q3952689
cites work: \(C^*\)-algebras of real rank zero
cites work: Almost Commuting Matrices Need not be Nearly Commuting
cites work: Simple \(C^*\)-algebras generated by isometries
cites work: K-theory for certain C*-algebras
cites work: Q4013262
cites work: Almost commuting Hermitian matrices.
cites work: Q3931913
cites work: On the classification of C*-algebras of real rank zero.
cites work: The structure of the irrational rotation \(C^*\)-algebra
cites work: On Inductive Limits of Matrix Algebras over the Two-Torus
cites work: On the classification of \(C^*\)-algebras of real rank zero. II
cites work: Abelian \(C^*\)-subalgebras of \(C^*\)-algebras of real rank zero and inductive limit \(C^*\)-algebras
cites work: AF embeddings of \(C(\mathbb{T}^ 2)\) with a prescribed \(K\)-theory
cites work: Almost Commuting Unitary Matrices
cites work: Invariants of almost commuting unitaries
cites work: Some unsolved problems of unknown depth about operators on Hilbert space
cites work: Ideals of Multiplier Algebras of Simple AF C ∗ -Algebras
cites work: Simple C ∗ -Algebras with Continuous Scales and Simple Corona Algebras
cites work: GENERALIZED WEYL-VON NEUMANN THEOREMS
cites work: Exponential rank of \(C^{\ast}\)-algebras with real rank zero and the Brown-Pedersen conjectures
cites work: Q4835027
cites work: Approximation by normal elements with finite spectra in \(C^*\)-algebras of real rank zero
cites work: The generalized Berg theorem and BDF-theorem
cites work: Homomorphisms From C(X) Into C*-Algebras
cites work: ALMOST NORMAL ELEMENTS
cites work: Classification of direct limits of even Cuntz-circle algebras
cites work: ALMOST MULTIPLICATIVE MORPHISMS AND THE CUNTZ ALGEBRA ${\mathcal O}_2$
cites work: On infinite simple \(C^*\)-algebras
cites work: K-Theory and Asymptotically Commuting Matrices
cites work: The noncommutative topology of one-dimensional spaces
cites work: Almost commuting matrices
cites work: Q3730459
cites work: Approximation by unitaries with finite spectrum in purely infinite \(C^*\)-algebras
cites work: Q4011084
cites work: Q4317853
cites work: Q3930248
cites work: Q3039940
cites work: On the structure of simple \(C^*\)-algebras tensored with a UHF-algebra
cites work: Classification of inductive limits of Cuntz algebras.
cites work: Q3933184
cites work: Q3324492
cites work: Certain \(C^*\)-algebras with real rank zero and their corona and multiplier algebras. I
cites work: On the Structure of Projections and Ideals of Corona Algebras
DOI: 10.1006/JFAN.1997.3214
description: scientific article; zbMATH DE number 1199743