From local to global triangularization
type: Item
instance of: scholarly article
title: From local to global triangularization
zbMATH Open document ID: 0902.47019
author: H. Radjavi
author: P. Rosenthal
published in: Journal of Functional Analysis
publication date: 1998-12-09T00:00:00Z
review text: A collection of bounded linear operators is said to be triangularizable if there exists a maximal subspace chain consisting of subspaces which are invariant under all operators in the collection. The main result of this paper asserts that a semigroup of operators in a Schatten \(p\)-class is triangularizable if every pair of operators in the semigroup is triangularizable. In other words, one can automatically pass from the local to global triangularization. The authors also establish a ``block triangularization'' theorem for algebras of compact operators, whose consequences include several necessary and sufficient conditions for triangularization of such algebras.
Mathematics Subject Classification ID: 47A66
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 1046933
zbMATH Keywords: block triangularization
zbMATH Keywords: maximal subspace domain
zbMATH Keywords: semigroup of operators
zbMATH Keywords: Schatten \(p\)-class
zbMATH Keywords: local to global triangularization
zbMATH Keywords: algebras of compact operators
reviewed by: Florian-Horia Vasilescu
MaRDI profile type: Publication
full work available at URL: jfan.1996.3069
OpenAlex ID: W1997459231
cites work: A nil algebra of bounded operators on Hilbert space with semisimple norm closure
cites work: Q3994330
cites work: Simultaneous Triangularization of Operators on a Banach Space
cites work: Q4024259
cites work: Q3917051
cites work: Invariant subspaces for the family of operators which commute with a completely continuous operator
cites work: Q3702021
cites work: Irreducible semigroups with multiplicative spectral radius
cites work: A Trace Condition Equivalent to Simultaneous Triangularizability
cites work: Q3032858
cites work: Q5686535
cites work: On transitive and reductive operator algebras
cites work: Super-Diagonal Forms for Compact Linear Operators
cites work: On representations of limit relations
cites work: On L-groups
cites work: Block triangularization of algebras of matrices
cites work: On L-semi-groups
DOI: 10.1006/JFAN.1996.3069
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description: scientific article; zbMATH DE number 1046933