On the semi-continuity of generalized inverses in Banach algebras
type: Item
instance of: scholarly article
title: On the semi-continuity of generalized inverses in Banach algebras
zbMATH Open document ID: 1106.47004
author: Qianglian Huang
author: Jipu Ma
published in: Linear Algebra and its Applications
publication date: 2006-12-07T00:00:00Z
review text: Let \(A\) be a Banach algebra. An element \(b \in A\) is called a reflexive generalized inverse for \(a \in A\) if \(a=aba\) and \(b=bab\). A reflexive generalized inverse \(a^\dagger\) of a \(C^*\)-algebra \(A\) is called the Moore--Penrose inverse of \(a\) if \((aa^\dagger)^*=aa^\dagger\) and \((a^\dagger a)^*=a^\dagger a\). Utilizing the method of \textit{Q.--L.\ Huang} and \textit{J.--P.\ Ma} [Linear Algebra Appl.\ 389, 355--364 (2004; Zbl 1072.47012)], the authors give sufficient and necessary conditions for the lower semicontinuity of the reflexive generalized inverse as a set-valued mapping in a unital Banach algebra. They also investigate the continuity of the Moore--Penrose inverse in a \(C^*\)-algebra and obtain some new criteria in operator theory.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 5077733
zbMATH Keywords: reflexive generalized inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: Banach algebra
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: lower semi-continuity
MaRDI profile type: Publication
full work available at URL: j.laa.2006.04.011
OpenAlex ID: W1972920830
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DOI: 10.1016/J.LAA.2006.04.011
description: scientific article; zbMATH DE number 5077733