Continuity of generalized inverses in Banach algebras
Volume 136 / 1999
Studia Mathematica 136 (1999), 197-227
DOI: 10.4064/sm-136-3-197-227
Abstract
The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.
