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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of the Weyl spectrum
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by Andrzej Pokrzywa PDF
Proc. Amer. Math. Soc. 92 (1984), 215-218 Request permission

Abstract:

It is shown that for each closed subset $\Omega$ of the semi-Fredholm domain of a bounded linear operator $T$ acting in a complex Hilbert space $H$ there exists a subspace of a finite codimension in $H$ such that the compression of $T - \lambda$ to this subspace is a left- or right-invertible operator for all $\lambda$ in $\Omega$. From this result we obtain a characterization of the Weyl spectrum of $T$.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 215-218
  • MSC: Primary 47A53; Secondary 47A10
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754706-6
  • MathSciNet review: 754706