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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## The closure of the invertibles in a von Neumann algebra

### Tom 69 / 1996

Colloquium Mathematicum 69 (1996), 157-165 DOI: 10.4064/cm-69-2-157-165

#### Streszczenie

In this paper we consider a subset Â 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 Â = A. In particular, we prove that Â = 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.

#### Autorzy

• Laura Burlando
• Robin Harte

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