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Approximating Fredholm operators on a nonseparable Hilbert space

  • Richard Bouldin (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500009721
  • Published online: 01 May 2009
Abstract
Abstract

This paper obtains a simple formula for the distance from a given operator to the set of invertible operators without requiring the underlying space to be separable. That formula is used to compute the distance to the Fredholm operators with a given index. These results require the further study of the concepts of essential nullity and essential deficiency, which permitted us to characterize the closure of the invertible operators. We also introduce a parameter called the modulus of Fredholmness.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

2.R. H. Bouldin , The essential minimum modulus, Indiana Univ. Math. J. 30 (1981), 513517.

3.R. H. Bouldin , Approximation by operators with fixed nullity, Proc. Amer. Math. Soc. 103 (1988), 141144.

5.R. H. Bouldin , Closure of invertible operators on a Hilbert space, Proc. Amer. Math. Soc. 108 (1990), 721726.

6.R. H. Bouldin , Approximation by semi-Fredholm operators with fixed nullity, Rocky Mountain J. Math. 20 (1990), 3950.

10.J. Feldman and R. V. Kadison , The closure of the regular operators in a ring of operators, Proc. Amer. Math. Soc. 5 (1954), 909916.

11.R. Harte , Regular boundary elements, Proc. Amer. Math. Soc. 99 (1987), 328330.

15.P. Y. Wu , Approximation by invertible and noninvertible operators, J. Approximation Theory 56 (1989), 267276.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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