A generalization of Banach's lemma and its applications to perturbations of bounded linear operators  

作　　者：WANG Zi DING Jiu WANG Yu-wen 

机构地区：[1]School of Mathematics Sciences,Harbin Normal University,Harbin 150025,China [2]School of Mathematics and Natural Sciences,The University of Southern Mississippi,Hattiesburg MS 39406-5043,USA [3]Academic Committee,Harbin Institute of Petroleum,Harbin 150027,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第2期363-369,共7页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(12001142).

摘　　要：Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

关 键 词：Banach lemma spectral radius generalized inverse perturbation analysis 

分 类 号：O177[理学—数学]