The generalized core-EP inverses involvoing projections in Banach *- algebra

Abstract

We investigate necessary and sufficient conditions under which the differences and products of two projections are generalized core-EP in-vertible. Then we present the representation of generalized core-EP inverse in a Banach *-algebra element by using related projections. Moreover, ex-pressions involving projections for the generalized core-EP inverse are given in a symmetric Banach *-algebra.