Continuity of generalized inverses in Banach algebras

Authors
Roch, S Silbermann, B
Citation
S. Roch et B. Silbermann, Continuity of generalized inverses in Banach algebras, STUD MATH, 136(3), 1999, pp. 197-227
Citations number
19
Categorie Soggetti
Mathematics
Journal title
STUDIA MATHEMATICA
ISSN journal
00393223 → ACNP
Volume
136
Issue
3
Year of publication
1999
Pages
197 - 227
Database
ISI
SICI code
0039-3223(1999)136:3<197:COGIIB>2.0.ZU;2-I
Abstract
The main topic of the paper is the continuity of several kinds of generaliz ed inversion of elements in a Banach algebra with identity. We introduce th e notion of asymptotic generalized invertibility and completely characteriz e sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.