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On closed subspaces of operator ranges


Authors: Robin Harte and Gerry Shannon
Journal: Proc. Amer. Math. Soc. 118 (1993), 171-173
MSC: Primary 47A05
DOI: https://doi.org/10.1090/S0002-9939-1993-1131035-8
MathSciNet review: 1131035
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Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient for the closure of a linear subspace to lie in the range of a bounded linear operator is a certain "bounded preimage property" for the operator.


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

  • [1] E. Albrecht and R. D. Mehta, Some remarks on local spectral theory, J. Oper. Theory 2 (1984), 285-317. MR 757436 (85m:47031)
  • [2] S. Goldberg, Unbounded linear operators, McGraw Hill, New York, 1966. MR 0200692 (34:580)
  • [3] R. E. Harte, Invertibility and singularity, Dekker, New York, 1988.
  • [4] Ju. N. Vladimirskiĭ, Observations on Calkin operators, Siberian Math. J. 17 (1976), 715-717. MR 0423109 (54:11090)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1131035-8
Keywords: Operator ranges, bounded sequences, Calkin property
Article copyright: © Copyright 1993 American Mathematical Society

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