On \(K\)-groups of operator algebra on the 1-shift space
type: Item
instance of: scholarly article
title: On \(K\)-groups of operator algebra on the 1-shift space
zbMATH Open document ID: 1157.19005
author: Qiaofen Jiang
author: Huaijie Zhong
publication date: 2008-11-17T00:00:00Z
review text: Their main result is to show that the \(K\)-theory groups \(K_0\) and \(K_1\) for the Banach algebra \(B(X_{GM2})\) of all bounded linear operators on the \(1\)-shift space \(X_{GM2}\) of \textit{W. T. Gowers} and \textit{B. Maurey} [Math. Ann. 307, No.~4, 543--568 (1997; Zbl 0876.46006)] are \(\mathbb Z\) and zero, respectively. For its proof, the six-term exact sequence of \(K\)-groups for a short exact sequence of \(B(X_{GM2})\) is computed explicitly, and for this, the \(K\)-groups of the Wiener algebra are also computed, and their generators are determined explicitly as well, and a characterization of Fredholm operators in \(B(X_{GM2})\) is also obtained.
reviewed by: Takahiro Sudo
Mathematics Subject Classification ID: 19K99
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 5366761
zbMATH Keywords: 1-shift space
zbMATH Keywords: operator algebra
zbMATH Keywords: \(K\)-group
zbMATH Keywords: Banach space
MaRDI profile type: Publication
full work available at URL: s10114-008-6471-2
OpenAlex ID: W2023482330
cites work: Banach spaces with small spaces of operators
cites work: K -Theory for Algebras of Operators on Banach Spaces
cites work: Some G-M-type Banach spaces and K-groups of operator algebras on them.
cites work: A BANACH SPACE WHOSE OPERATOR ALGEBRA HAS K0-GROUP ℚ
cites work: Q4520088
cites work: Topological invariants of the maximal ideal space of a Banach algebra
cites work: Q3660524
cites work: Q5660202
DOI: 10.1007/S10114-008-6471-2
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 5366761