# The closure of the invertibles in a von Neumann algebra

Colloquium Mathematicae (1996)

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

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topBurlando, 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 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.},

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 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.

LA - eng

KW - generalized inverse; closure of the invertibles; von Neumann algebra

UR - http://eudml.org/doc/210332

ER -

## References

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