Mohammed Berkani, Department of Mathematics, Science Faculty of Oujda, University Mohammed I, Team EQUITOMI, SFO, Laboratory MATSI, EST, e-mail: berkanimo@aim.com; Hassan Zariouh, Department of Mathematics, Science Faculty of Meknes, University Moulay Ismail, e-mail: h.zariouh@yahoo.fr
Abstract: An operator $T$ acting on a Banach space $X$ possesses property $(\gw)$ if $\sigma_a(T)\setminus\sigma_{\SBF_+^-}(T)= E(T), $ where $\sigma_a(T)$ is the approximate point spectrum of $T$, $\sigma_{\SBF_+^-}(T)$ is the essential semi-B-Fredholm spectrum of $T$ and $E(T)$ is the set of all isolated eigenvalues of $T.$ In this paper we introduce and study two new properties $(\b)$ and $(\gb)$ in connection with Weyl type theorems, which are analogous respectively to Browder's theorem and generalized Browder's theorem. Among other, we prove that if $T$ is a bounded linear operator acting on a Banach space $X$, then property $(\gw)$ holds for $T$ if and only if property $(\gb)$ holds for $T$ and $E(T)=\Pi(T),$ where $\Pi(T)$ is the set of all poles of the resolvent of $T.$
Keywords: B-Fredholm operator, Browder's theorem, generalized Browder's theorem, property $(\b)$, property $(\gb)$
Classification (MSC 2000): 47A53, 47A10, 47A11
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
