Generalized Weyl's theorem and quasi-affinity
Volume 198 / 2010
Studia Mathematica 198 (2010), 105-120
MSC: Primary 47A11, 47A53; Secondary 47A10.
DOI: 10.4064/sm198-2-1
Abstract
A bounded operator $T\in L(X)$ acting on a Banach space $X$ is said to satisfy generalized Weyl's theorem if the complement in the spectrum of the B-Weyl spectrum is the set of all eigenvalues which are isolated points of the spectrum. We prove that generalized Weyl's theorem holds for several classes of operators, extending previous results of Istrăţescu and Curto–Han. We also consider the preservation of generalized Weyl's theorem between two operators $T\in L(X)$, $S\in L(Y)$ intertwined or asymptotically intertwined by a quasi-affinity $A\in L(X,Y)$.
