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Proceedings of the American Mathematical Society

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

 

 

A characterization of the Weyl spectrum


Author: Andrzej Pokrzywa
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1984-0754706-6
Keywords: Semi-Fredholm domain, Weyl spectrum, compression of an operator
Article copyright: © Copyright 1984 American Mathematical Society