The Core Inverse in a Banach Algebra with Involution

2022/09/21 by Sheibani, Marjan, Chen, Huanyin
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2209.10090

Abstract

We present new additive results for the core inverse in a Banach algebra with involution. We obtain necessary and sufficient conditions under which the sum of two core invertible elements in a Banach algebra with involution is core invertible. Then we apply our results to block complex matrices and obtain certain conditions under which a block complex is core invertible. These generalize many known results, e.g.,~\cite[Theorem 4.3]XCZ, ~\cite[Theorem 2.5]XS.

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