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.
@article{bwmeta1.element.bwnjournal-article-smv136i3p197bwm,
author = {Steffen Roch and Bernd Silbermann},
title = {Continuity of generalized inverses in Banach algebras},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {197-227},
zbl = {0962.47002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i3p197bwm}
}
Roch, Steffen; Silbermann, Bernd. Continuity of generalized inverses in Banach algebras. Studia Mathematica, Tome 133 (1999) pp. 197-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i3p197bwm/
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