A bounded linear operator T ∈ L(X) on a Banach space X is said to satisfy "Weyl''s theorem" if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if T is a paranormal operator on a Hilbert space, then T + K satisfies Weyl''s theorem for every algebraic operator K which commutes with T.
AIENA, P., GUILLEN, J. (2007). Weil's theorem for perturbations of paranormal operators. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135, 2443-2451.
Weil's theorem for perturbations of paranormal operators
AIENA, Pietro;
2007-01-01
Abstract
A bounded linear operator T ∈ L(X) on a Banach space X is said to satisfy "Weyl''s theorem" if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if T is a paranormal operator on a Hilbert space, then T + K satisfies Weyl''s theorem for every algebraic operator K which commutes with T.
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