On the semi-continuity of generalized inverses in Banach algebras |
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Authors: | Qianglian Huang Jipu Ma |
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Institution: | a College of Mathematics, Yangzhou University, Yangzhou 225002, China b Yuan-Yung Tseng Functional Analysis Research Center, Harbin Normal University, Harbin 150025, China |
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Abstract: | 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. |
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Keywords: | 15A09 46H05 47H05 |
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