The closure of the invertibles in a von Neumann algebra

Laura Burlando; Robin Harte

Colloquium Mathematicae (1996)

  • Volume: 69, Issue: 2, page 157-165
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Burlando, Laura, and Harte, Robin. "The closure of the invertibles in a von Neumann algebra." Colloquium Mathematicae 69.2 (1996): 157-165. <http://eudml.org/doc/210332>.

@article{Burlando1996,
abstract = {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.},
author = {Burlando, Laura, Harte, Robin},
journal = {Colloquium Mathematicae},
keywords = {generalized inverse; closure of the invertibles; von Neumann algebra},
language = {eng},
number = {2},
pages = {157-165},
title = {The closure of the invertibles in a von Neumann algebra},
url = {http://eudml.org/doc/210332},
volume = {69},
year = {1996},
}

TY - JOUR
AU - Burlando, Laura
AU - Harte, Robin
TI - The closure of the invertibles in a von Neumann algebra
JO - Colloquium Mathematicae
PY - 1996
VL - 69
IS - 2
SP - 157
EP - 165
AB - 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.
LA - eng
KW - generalized inverse; closure of the invertibles; von Neumann algebra
UR - http://eudml.org/doc/210332
ER -

References

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