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Classes of operators satisfying a-Weyl's theorem

Pietro Aiena (2005)

Studia Mathematica

In this article Weyl’s theorem and a-Weyl’s theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl’s theorem and a-Weyl’s theorem for T* are equivalent, and analogously, if T* has SVEP then Weyl’s theorem and a-Weyl’s theorem for T are equivalent. From this result we deduce that a-Weyl’s theorem holds for classes of operators for which the quasi-nilpotent part H₀(λI...

Convergence of approximation methods for eigenvalue problem for two forms

Teresa Regińska (1984)

Aplikace matematiky

The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space X . We investigate some approximation methods generated by sequences of forms a n and b n defined on a dense subspace of X . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.

Corrigendum and addendum: "On the axiomatic theory of spectrum II"

J. Koliha, M. Mbekhta, V. Müller, Pak Poon (1998)

Studia Mathematica

The main purpose of this paper is to correct the proof of Theorem 15 of [4], concerned with the stability of the class of quasi-Fredholm operators under finite rank perturbations, and to answer some open questions raised there.

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