English

The g-Drazin invertibility in a Banach algebra

Rings and Algebras 2022-03-16 v1

Abstract

We present necessary and sufficient conditions under which the anti-triangular matrix (ab10)\left( \begin{array}{cc} a&b 1&0 \end{array} \right) over a Banach algebra has g-Drazin inverse. New additive results for g-Drazin inverse are obtained. Then we apply our results to 2×22\times 2 operator matrices and generalize many known results, e.g.,~\cite[Theorem 2.2]{D}, ~\cite[Theorem 2.1]{YL} and \cite[Theorem 4.1]{Y}.

Keywords

Cite

@article{arxiv.2203.07568,
  title  = {The g-Drazin invertibility in a Banach algebra},
  author = {Huanyin Chen and Marjan Sheibani},
  journal= {arXiv preprint arXiv:2203.07568},
  year   = {2022}
}