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Continuity of the generalized kernel and range of semi-Fredholm operators

  • M. Ó Searcóid (a1) and T. T. West (a2)

Let X denote a Banach space over the complex field ℂ and let B(X) be the Banach algebra of all bounded linear operators on X. If T ε B(X), we write n(T) = dim ker (T) and d(T) = codim T(X). Suppose that Y is a subspace invariant under T; then TY will denote the restriction of T to Y and Y the operator on X/Y defined by

Y: x/Y →(Tx)/Y

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[3] R. H. Homer . Regular extensions and the solvability of operator equations. Proc. Amer. Math. Soc. 12 (1961), 415418.

[5] T. Kato . Perturbation Theory for Linear Operators (Springer-Verlag, 1966).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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