On the \(K_ 0\) groups of nest algebras
type: Item
instance of: scholarly article
title: On the \(K_ 0\) groups of nest algebras
zbMATH Open document ID: 0682.46046
DOI: 10.1007/BF00538430
author: David R. Pitts
published in: \(K\)-Theory
publication date: 1989-01-01T00:00:00Z
review text: The \(K_ 0\) functor is computed on a class of subalgebras of \({\mathcal B}({\mathcal H})\), the so called nest subalgebras. Such algebras \(A(\beta)\) are associated to given nests \(\beta\) of projections in \(B({\mathcal H})\). Define a linear mapping \(\phi\) of \({\mathcal B}({\mathcal H})\) by \(\phi (X)=0\) if \(\beta\) is continuous, and \(\sum q_ iXq_ i\) otherwise where \(\{q_ i\}\) is the set of atoms of \(\beta\). Let \(Q=\phi (I)\) and \(D(\beta)=A(\beta)\cap A(\beta)^*\). The author proves that the homomorphism \(\phi: A(\beta)\to QD(\beta)Q\) induces an isomorphism, \(\phi_*: K_ 0(A(\beta))\to K_ 0(QD(\beta)Q)\). If \(\Lambda\) denotes the set of finite-dimensional atoms in \(\beta\), then the author proves that \(K_ 0(A(\beta))\simeq {\bar \oplus}_{q\in \Lambda}{\mathbb{Z}}\) where \({\bar \oplus}_{q\in \Lambda}{\mathbb{Z}}=\{g: \Lambda \to {\mathbb{Z}}:\quad \sup_{\Lambda}| g(q)/tr(q)| <\infty \}.\)
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A67
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 4117247
zbMATH Keywords: minimal projection
zbMATH Keywords: \(K_ 0\) functor
zbMATH Keywords: nest subalgebras
zbMATH Keywords: finite- dimensional atoms
reviewed by: Palle Jorgensen
MaRDI profile type: Publication
cites work: Compact perturbations of reflexive algebras
cites work: Q3688957
cites work: Analyticity in Operator Algebras
cites work: Interpolation problems in nest algebras
cites work: A class of C*-algebras and topological Markov chains II: Reducible chains and the Ext-functor for C*-algebras
cites work: Approximate Unitary Equivalence of Continuous Nests
cites work: Similarity and compact perturbations of nest algebras.
cites work: Unitary invariants for nests
cites work: Q3903539
cites work: Nest-subalgebras of von Neumann algebras
cites work: Q5590313
cites work: Triangular Operator Algebras: Fundamentals and Hyperreducible Theory
cites work: Cohomology and Perturbations of Nest Algebras
cites work: Q3711197
cites work: Nest algebras and similarity transformations
cites work: Factorization problems for nests: Factorization methods and characterizations of the universal factorization property
cites work: Q3876492
cites work: Q3881382
description: scientific article; zbMATH DE number 4117247