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Title

The closure of the invertibles in a von Neumann algebra

Authors 1, 2

Affiliations

  1. Dipartimento di Matematica, università di Genova, via Dodecaneso 35, 16146 Genova, Italy
  2. Queen's University, Belfast BT7 1NN, Northern Ireland, UK

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.

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Colloquium Mathematicum
1996/69/2
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Pages:
157-165
Main language of publication
English
Received
1994-07-04
Published
1996
Exact and natural sciences