Sinclair type inequalities for the local spectral radius and related topics
type: Item
instance of: scholarly article
title: Sinclair type inequalities for the local spectral radius and related topics
zbMATH Open document ID: 0648.47005
DOI: 10.1007/BF02766214
author: Khristo N. Boyadzhiev
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Using a result of \textit{B. Ya. Levin} [Amer. Math. Soc. 1964, VIII, 493 p. (1964; Zbl 0152.067)] concerning the class P of entire functions, the author obtains a general pointwise inequality for the class of all bounded operators A on a Banach space X with real spectra such that \[ \| e^{itA}\| =O(| t|^ p)\text{ for some } p>0 \] when \(t\in {\mathbb{R}}\), \(| t| \to \infty.\) As a corollary of his result, he shows that \[ \| Ax\| \leq \| x\| r(A+iB,x), \] where A and B are commuting Hermitian operators on X and r(T,x) is the local spectral radius of T at x is defined as \[ r(T,x):=\limsup_{n\to \infty}\| T^ nx\|^{1/n}. \] In the particular case, when \(B=0\), he obtains the Sinclair lemma [Am. Math. Month. 78, 871-873 (1971)] for Hermitian operators on a Banach space.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 4058232
zbMATH Keywords: local spectral radius
zbMATH Keywords: Sinclair lemma
zbMATH Keywords: Hermitian operators on a Banach space
MaRDI profile type: Publication
cites work: On some classes of generalized spectral operators
cites work: Q5550698
cites work: Dissipative Mappings and Well-Behaved Derivations
cites work: Q5833361
cites work: Q5608364
cites work: Unbounded derivations of \(C^*\)-algebras II
cites work: On Bernstein's Inequality and the Norm of Hermitian Operators
cites work: Optimal Landau-Kolmogorov inequalities for dissipative operators in Hilbert and Banach spaces
cites work: Seminormal operators
cites work: Q5584224
cites work: Commutators and normal operators
cites work: Q3254057
cites work: On the class of paranormal operators
cites work: Q3906645
cites work: Q5633139
cites work: Q3848344
cites work: Dissipative operators in a Banach space
cites work: The Resolvent of a Hermitian Operator on a Banach Space
cites work: Q5637340
cites work: The Norm of a Hermitian Element in a Banach Algebra
full work available at URL: https://doi.org/10.1007/bf02766214
OpenAlex ID: W2078966783
description: scientific article; zbMATH DE number 4058232