The characterizations and representations for the generalized inverses with prescribed idempotents in Banach algebras
Jianbing Cao, Yifeng Xue · Filomat · 2013
In this paper, we investigate the various different generalized inverses in a Banach algebra with respect to prescribed two idempotents p and q. Some new characterizations and explicit representations for these generalized inverses, such as a(2)p,q, a(1,2)p,q and a(2,l)p,q will be presented. The obtained results extend and generalize some well-known results for matrices or operators. .