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Generalizations of semi-Fredholm operators


Author: Richard Bouldin
Journal: Proc. Amer. Math. Soc. 123 (1995), 3757-3764
MSC: Primary 47A53; Secondary 47A05, 47A58
DOI: https://doi.org/10.1090/S0002-9939-1995-1301011-2
MathSciNet review: 1301011
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Abstract: On nonseparable Hilbert spaces there are multiple sets of operators that are analogous to the semi-Fredholm operators on a separable space. We develop the properties of these sets and relate those properties to some recent research. We conclude with a theorem that indicates precisely how far one can go from a given generalized semi-Fredholm operator (or generalized Fredholm operator) and retain the property of generalized semi-Fredholmness (or generalized Fredholmness).


References [Enhancements On Off] (What's this?)

  • [1] C. Apostol, L. A. Fialkow, D. A. Herrero, and D. Voiculescu, Approximation of Hilbert space operators, Vol. II, Pitman, Boston, 1984. MR 735080 (85m:47002)
  • [2] R. H. Bouldin, The essential minimum modulus, Indiana Univ. Math. J. 30 (1981), 513-517. MR 620264 (82i:47001)
  • [3] -, Approximation by operators with fixed nullity, Proc. Amer. Math. Soc. 103 (1988), 141-144. MR 938658 (89g:47003)
  • [4] -, The distance to operators with a fixed index, Acta Sci. Math. (Szeged) 54 (1990), 139-143. MR 1073428 (91k:47022)
  • [5] -, Closure of invertible operators on a Hilbert space, Proc. Amer. Math. Soc. 108 (1990), 721-726. MR 1000147 (90m:47009)
  • [6] -, Approximating Fredholm operators on a nonseparable Hilbert space, Glasgow Math. J. 35 (1993), 167-178. MR 1220559 (94c:47013)
  • [7] -, Distance to invertible operators without separability, Proc. Amer. Math. Soc. 116 (1992), 489-497. MR 1097336 (92m:47032)
  • [8] -, Largely singular operators, J. Math. Anal. Appl. 188 (1994), 141-150. MR 1301722 (95h:47003)
  • [9] L. Burlando, Distance formulas on operators whose kernel has fixed Hilbert dimension, Rend. Mat. (7) 10 (1990), 209-238. MR 1076155 (91j:47014)
  • [10] R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972. MR 0361893 (50:14335)
  • [11] G. Edgar, J. Ernest, and S. G. Lee, Weighing operator spectra, Indiana Univ. Math. J. 121 (1971), 61-80. MR 0417836 (54:5884)
  • [12] R. Harte, Regular boundary elements, Proc. Amer. Math. Soc. 99 (1987), 328-330. MR 870795 (88d:46088)
  • [13] D. A. Herrero, Approximation of Hilbert space operators, Vol. I, Pitman, Boston, 1982. MR 676127 (85m:47001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1301011-2
Keywords: Semi-Fredholm operator, nonseparable Hilbert space, essential nullity, modulus of invertibility, stability theorem
Article copyright: © Copyright 1995 American Mathematical Society

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