Domination conditions and spectral multiplicity of operators
type: Item
instance of: scholarly article
title: Domination conditions and spectral multiplicity of operators
zbMATH Open document ID: 1261.47047
published in: Acta Mathematica Hungarica
publication date: 2012-02-13T00:00:00Z
review text: Let \(X\) be a Banach space, \(A: X \to X\) be a bounded linear operator. The quantity \(\mu(A) = \inf\{ \dim E: \text{span}\{A^nE \}_{n=0}^\infty = X\}\) is called the spectral multiplicity of \(A\). For a direct sum of operators, the following inequalities are known: \(\max\{\mu(A), \mu(B)\} \leq \mu(A \oplus B) \leq \mu(A) + \mu(B)\). In the paper under review, developing technique from \textit{M. T. Karaev} [Arch. Math. 93, No. 2, 147--152 (2009; Zbl 1189.46041)], the author studies conditions under which \(\mu(A\oplus B) = \mu(A) + \mu(B)\).
reviewed by: Vladimir Kadets
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47B48
zbMATH DE Number: 6006169
zbMATH Keywords: spectral multiplicity
zbMATH Keywords: direct sum of operators
zbMATH Keywords: shift operator
zbMATH Keywords: Banach algebra
zbMATH Keywords: domination condition
author: Mubariz T. Karaev
MaRDI profile type: Publication
full work available at URL: s10474-011-0128-9
OpenAlex ID: W1985136756
cites work: Q3254057
cites work: Multiplicity of direct sums of operators on Banach spaces
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cites work: Some applications of the Duhamel product
cites work: Q3068268
cites work: Banach algebra techniques for spectral multiplicity
cites work: Q5785370
DOI: 10.1007/S10474-011-0128-9
description: scientific article; zbMATH DE number 6006169