In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman and Kadison's characterization of the closure of the invertibles in a von Neumann algebra and a more recent characterization of the closure of the invertibles in the bounded linear operators on a Hilbert space.
@article{bwmeta1.element.bwnjournal-article-cmv69i2p157bwm,
author = {Laura Burlando and Robin Harte},
title = {The closure of the invertibles in a von Neumann algebra},
journal = {Colloquium Mathematicae},
volume = {70},
year = {1996},
pages = {157-165},
zbl = {0848.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv69i2p157bwm}
}
Burlando, Laura; Harte, Robin. The closure of the invertibles in a von Neumann algebra. Colloquium Mathematicae, Tome 70 (1996) pp. 157-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv69i2p157bwm/
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