Mediterranean Journal of Mathematics

, Volume 4, Issue 2, pp 215–228

Generalized Browder’s Theorem and SVEP

Authors

    • Dipartimento di Matematica ed Applicazioni Facoltà di IngegneriaUniversità di Palermo
  • Orlando Garcia
    • Departamento de Matemáticas Facultad de CienciasUniversidad UDO
Article

DOI: 10.1007/s00009-007-0113-2

Cite this article as:
Aiena, P. & Garcia, O. MedJM (2007) 4: 215. doi:10.1007/s00009-007-0113-2

Abstract.

A bounded operator \(T \in L(X), X\) a Banach space, is said to verify generalized Browder’s theorem if the set of all spectral points that do not belong to the B-Weyl’s spectrum coincides with the set of all poles of the resolvent of T, while T is said to verify generalized Weyl’s theorem if the set of all spectral points that do not belong to the B-Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues. In this article we characterize the bounded linear operators T satisfying generalized Browder’s theorem, or generalized Weyl’s theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0IT) as λ belongs to certain subsets of \({\mathbb{C}}\). In the last part we give a general framework for which generalized Weyl’s theorem follows for several classes of operators.

Mathematics Subject Classification (2000).

Primary 47A10, 47A11Secondary 47A53, 47A55

Keywords.

SVEPFredholm theorygeneralized Weyl’s theorem and generalized Browder’s theorem

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007