Spectral properties of elements of normed algebras and invariant subspaces
type: Item
instance of: scholarly article
title: Spectral properties of elements of normed algebras and invariant subspaces
zbMATH Open document ID: 0569.47005
DOI: 10.1007/BF01077836
publication date: 1984-01-01T00:00:00Z
review text: Let A be a normed algebra with norm \(\| \|_ A\), \(M\subset A\) be a bounded subset, M' be the commutant of M, A(M) be the subalgebra of A, generated by M, \(M^ n\) be the set of all products of n elements from M, \(\| M\| =\sup \{\| a\|_ A:a\in M\}\) and \(r(M)=\lim \| M^ n\|^{1/n}.\) An element a from a subalgebra B of A is called Lie radical if \(r(ab-ba)=0\) for each \(b\in B.\) In addition to the other results the conditions in order that the union of two triangulable families of compact operators from L(X) (the algebra of all bounded linear operators on a Banach space X with dim X 2) is triangulable and for given subsets S,M\(\subset L(X)\) the algebra A(S\(\cup M)\) and its commutant have a common nontrivial invariant subspace are described. Moreover it is stated that any Lie radical compact operator from a subalgebra \(B\subset L(X)\) is Lie radical for \(cl_{L(X)}A(B\cup B').\)
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 3909129
zbMATH Keywords: Lie radical
zbMATH Keywords: triangulable families of compact operators
zbMATH Keywords: common nontrivial invariant subspace
author: Yurii V. Turovskii
reviewed by: Mart Abel
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3909129