We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel....
We present new results related to various equivalents of the mixed-type reverse order law for the Moore-Penrose inverse for operators on Hilbert spaces. Recent finite-dimensional results of Tian are extended to Hilbert space operators.
Let be an operator acting on a Banach space , let and be respectively the spectrum and the B-Weyl spectrum of . We say that satisfies the generalized Weyl’s theorem if , where is the set of all isolated eigenvalues of . The first goal of this paper is to show that if is an operator of topological uniform descent and is an accumulation point of the point spectrum of then does not have the single valued extension property at , extending an earlier result of J. K. Finch and a...
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