Generalized Hirano inverses in Banach Algebra

Huanyin chen, Sarjan Sheibani

Let $A$ be a Banach Algebra, we say that $a\in A$ has generalized Hirano inverse if there exists some $b\in A$ such that $b=b.a.b,a.b=b.a$ and $a-a^2.b$ is quasi nil potent, if a…