The Core Inverse in a Banach Algebra with Involution
Rings and Algebras
2022-09-22 v1
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}.
Cite
@article{arxiv.2209.10090,
title = {The Core Inverse in a Banach Algebra with Involution},
author = {Marjan Sheibani and Huanyin Chen},
journal= {arXiv preprint arXiv:2209.10090},
year = {2022}
}