Similarity invariant subspaces and Lie ideals in operator algebras.
type: Item
instance of: scholarly article
title: Similarity invariant subspaces and Lie ideals in operator algebras.
zbMATH Open document ID: 1042.47050
DOI: 10.1007/BF01217529
author: Yanyan Li
published in: Integral Equations and Operator Theory
publication date: 2003-07-15T00:00:00Z
review text: Let \(X\) be a complex Banach space and \(L(X)\) be the algebra of all linear bounded operators \(T: X \rightarrow X\) endowed with the uniform operator topology. \(GL(X)\) denotes the group of all invertible operators belonging to \(L(X)\). A closed subspace \(J\) of \(L(X)\) is called a Lie ideal if \([A,B]=AB -BA \in J\) for all \(A \in J\) and \(B \in L(X)\). In this paper, the authors obtain a full description of nontrivial Lie ideals (and hence a complete list of \(GL(X)\)-invariant subspaces) for the spaces \(l^{p}\) \((1 \geq p < {\infty})\) of \(p\)-summable sequences and the space \(c_{0}\) of sequences converging to zero.
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 47L05
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47L10
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 1890573
zbMATH Keywords: Lie ideals
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: invariant subspace
zbMATH Keywords: commutator
zbMATH Keywords: rich in commutators
MaRDI profile type: Publication
cites work: Q5660222
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full work available at URL: https://doi.org/10.1007/bf01217529
OpenAlex ID: W2032514477
description: scientific article; zbMATH DE number 1890573