MATHEMATICA BOHEMICA, Vol. 133, No. 2, pp. 157-166 (2008)

A note on the $a$-Browder's and $a$-Weyl's theorems

M. Amouch, H. Zguitti

M. Amouch, Department of Mathematics, Faculty of Science of Semlalia, B.O. 2390 Marrakesh, Morocco, e-mail:; H. Zguitti, Department of Mathematics, Faculty of Science of Rabat, B.O. 1014 Rabat, Morocco, e-mail:

Abstract: Let $T$ be a Banach space operator. In this paper we characterize $a$-Browder's theorem for $T$ by the localized single valued extension property. Also, we characterize $a$-Weyl's theorem under the condition $E^a(T)=\pi ^a(T),$ where $E^a(T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $\pi ^a(T)$ is the set of all left poles of $T.$ Some applications are also given.

Keywords: B-Fredholm operator, Weyl's theorem, Browder's thoerem, operator of Kato type, single-valued extension property

Classification (MSC2000): 47A53, 47A10, 47A11

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]
© 2008–2010 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition