The Bohr-Favard inequalities for operators
type: Item
instance of: scholarly article
title: The Bohr-Favard inequalities for operators
zbMATH Open document ID: 1191.47015
DOI: 10.3103/S1066369X09120020
author: K. A. Sintyaeva
author: Anatoly G. Baskakov
published in: Russian Mathematics
publication date: 2010-01-12T00:00:00Z
review text: The problem under consideration is to estimate the value \(\|A^{-1}\|\) for the generator \(iA\) of an arbitrary isometric group of operators \(T:{\mathbb R} \to \text{End}X\) under the assumption \(0\in\mathbb{C}\setminus \sigma(A)\). One of the main results of the paper is that, if \(\sigma(A)\subset [\alpha,\infty)\), where \(\alpha>0\) and \(\alpha\in\sigma(A)\), then \(\|A^{-1}\|=r(A^{-1})=1/\alpha\), where \(r(A^{-1})\) is the spectral radius of the operator \(A^{-1}\).
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 5655839
zbMATH Keywords: resolvent
zbMATH Keywords: generator
zbMATH Keywords: isometric group of operators
zbMATH Keywords: perturbation theory
MaRDI profile type: Publication
cites work: Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators
cites work: Q3862621
cites work: Q4244341
cites work: SPECTRAL ANALYSIS OF PERTURBED NONQUASIANALYTIC AND SPECTRAL OPERATORS
description: scientific article; zbMATH DE number 5655839