Distance to invertible linear operators without separability
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- by Richard Bouldin
- Proc. Amer. Math. Soc. 116 (1992), 489-497
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097336-6
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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.References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 489-497
- MSC: Primary 47A58; Secondary 47D15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097336-6
- MathSciNet review: 1097336