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A stability theorem on quasi-reflexive operators


Author: Tsu-Chih Wu
Journal: Proc. Amer. Math. Soc. 65 (1977), 252-254
MSC: Primary 47A05; Secondary 47B30
DOI: https://doi.org/10.1090/S0002-9939-1977-0451003-X
MathSciNet review: 0451003
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Abstract | References | Similar Articles | Additional Information

Abstract: A range-closed bounded linear operator between Banach spaces is quasi-reflexive if both its kernel and cokernel are quasi-reflexive spaces. Under suitable conditions, if an operator is sufficiently close to a quasi-reflexive operator, it is itself quasi-reflexive.


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

  • [1] P. Civin and B. Yood, Quasi-reflexive spaces, Proc. Amer. Math. Soc. 8 (1957), 906-911. MR 0090020 (19:756a)
  • [2] R. S. Palais et al., Seminar on the Atiyah-Singer index theorem, Ann. of Math. Studies, no. 57, Princeton Univ. Press, Princeton, N. J., 1965. MR 0198494 (33:6649)
  • [3] K. W. Yang, The generalized Fredholm operators, Trans. Amer. Math. Soc. 216 (1976), 313-326. MR 0423114 (54:11095)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0451003-X
Keywords: Banach spaces, complementary subspace, quasi-reflexive, double-splitting, kernel, cokernel
Article copyright: © Copyright 1977 American Mathematical Society

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