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Pseudo core invertibility in Banach *-algebras and its applications (2209.10124v1)
Published 21 Sep 2022 in math.RA
Abstract: We present new additive results for the pseudo core inverse in a Banach algebra with involution. The necessary and sufficient conditions under which the sum of two pseudo core invertible elements in Banach *-algebra is pseudo core invertible are obtained. As an application, the pseudo core invertibility for block complex matrices is investigated. These extend the main results of pseudo core invertibility of Gao and Chen [Comm. Algebra, 46(2018), 38--50].
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