Core inverse in Banach algebras

Abstract

We define and characterize the core inverse in the context of Banach algebras. The Banach space operator case is also considered. Using the core inverse, we present new characterizations of EP Banach space operators and EP Banach algebra elements. The dual core inverse for Banach algebra elements is presented too. Some new characterizations of co-EP Banach algebra elements are given by means the core inverse and dual core inverse. Keywords Core inverse • Group inverse • Moore-Penrose inverse • Banach algebra Mathematics Subject Classification 46H05 • 47A05 • 15A09

Co-EP-Ness and EP-Ness Involving the Inverse along an Element

“…This invertibility was also considered in [12]. More results about co-EP properties can be seen in [8,10,[14][15][16][17].…”