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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Closure of invertible operators on a Hilbert space

Author: Richard Bouldin
Journal: Proc. Amer. Math. Soc. 108 (1990), 721-726
MSC: Primary 47A05; Secondary 47D99
MathSciNet review: 1000147
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Abstract: Although most of the characterizations of the closure of the invertible operators on a separable Hilbert space do not extend to a nonseparable Hilbert space, this note gives a characterization for an arbitrary Hilbert space that generalizes the separable case in a natural way. The new concept of essential nullity, which facilitates this characterization, should find other applications.

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PII: S 0002-9939(1990)1000147-9
Keywords: Invertible operator, closure, ring of operators, nonseparable Hilbert space, essential nullity
Article copyright: © Copyright 1990 American Mathematical Society