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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Distance to invertible linear operators without separability


Author: Richard Bouldin
Journal: Proc. Amer. Math. Soc. 116 (1992), 489-497
MSC: Primary 47A58; Secondary 47D15
MathSciNet review: 1097336
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Abstract: The formula for the distance from a given operator to the invertible operators on a separable Hilbert space is not true if the underlying Hilbert space is not required to be separable. This paper obtains inequalities for that distance in the latter situation. This requires a new concept called the modulus of invertibility, and further study of the concepts of essential nullity and essential deficiency, which permitted us to characterize the closure of the invertible operators.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1097336-6
Keywords: Invertible operator, ring of operators, nonseparable Hilbert space, essential nullity, essential deficiency, modulus of invertibility
Article copyright: © Copyright 1992 American Mathematical Society