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2 results

  • STRICTLY SINGULAR PERTURBATION OF ALMOST SEMI-FREDHOLM LINEAR RELATIONS IN NORMED SPACES

  • T. ÁLVAREZ
  • Journal:
    Glasgow Mathematical Journal / Volume 56 / Issue 1 / January 2014
    Published online by Cambridge University Press:
    13 August 2013, pp. 211-219
    Print publication:
    January 2014
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  • In this paper, we introduce the notions of almost upper semi-Fredholm and strictly singular pairs of subspaces and show that the class of almost upper semi-Fredholm pairs of subspaces is stable under strictly singular pairs perturbation. We apply this perturbation result to investigate the stability of almost semi-Fredholm multi-valued linear operators in normed spaces under strictly singular perturbation as well as the behaviour of the index under perturbation.

  • ON ALMOST SEMI-FREDHOLM LINEAR RELATIONS IN NORMED SPACES

  • T. ÁLVAREZ
  • Journal:
    Glasgow Mathematical Journal / Volume 47 / Issue 1 / January 2005
    Published online by Cambridge University Press:
    31 January 2005, pp. 187-193
    Print publication:
    January 2005
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  • We give characterisations of the linear relations that are injective and open (respectively, almost open with dense range) in terms of the stability of the nullity (respectively, of the deficiency). Results of Mbekhta about bounded operators in Banach spaces (J. Operator Theory35 (1996), 191–201) are covered.