On the semi-continuity of generalized inverses in Banach algebras

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• 作者：Qianglian Huang and Jipu Ma
• 关键词：Reflexive generalized inverse ; Moore– ; Penrose inverse ; Banach algebra ; C^*-algebra ; Lower semi-continuity
• 刊名：Linear Algebra and its Applications
• 出版年：2006
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 November 2006
• 卷：419
• 期：1
• 页码：172-179
• 文件大小：130 K

摘要

The main purpose of this paper is to study the continuity of several kinds of generalized inverses of elements in a Banach algebra with identity. We first obtain a sufficient and necessary condition for the lower semi-continuity of reflexive generalized inverses as set-valued mappings. Based on this result, we characterize the continuity of the Moore–Penrose inverse in a C^*-algebra and therefore, derive some new and well-known criteria in operator theory.