Closure of invertible operators on a Hilbert space

Bouldin, Richard

doi:10.1090/S0002-9939-1990-1000147-9

Closure of invertible operators on a Hilbert space
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Proc. Amer. Math. Soc. 108 (1990), 721-726 Request permission

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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