Weil's theorem for perturbations of paranormal operators

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.