Weyl Type Theorems and Restrictions

In this paper we show that for a bounded linear operator T∈L(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T\in L(X)}$$\end{document} acting on a Banach space X, the study of generalized Weyl’s theorem for T can be reduced to the study of generalized Weyl’s theorem for some restrictions of T.