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Generalized spectrum and a problem of Apostol

Author: Mostafa Mbekhta
Journal: Proc. Amer. Math. Soc. 118 (1993), 857-859
MSC: Primary 47A10
MathSciNet review: 1145948
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Abstract: We give a complete answer to a question of Apostol concerning the asymptotic behaviour of the reduced minimum modulus of a bounded operator on Hilbert space.

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

  • [1] C. Apostol, The reduced minimum modulus, Michigan Math. J. 32 (1985), 279-294. MR 803833 (87a:47003)
  • [2] T. Kato, Perturbation theory for linear operators, Springer, New York, 1966. MR 0203473 (34:3324)
  • [3] M. Mbekhta, Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), 159-175. MR 901662 (88i:47010)
  • [4] -, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105. MR 1002122 (91a:47004)

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Keywords: Generalized spectrum, reduced minimum modulus
Article copyright: © Copyright 1993 American Mathematical Society

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