On generalized property for bounded linear operators
Volume 212 / 2012
Studia Mathematica 212 (2012), 141-154
MSC: Primary 47A10, 47A11; Secondary 47A53, 47A55.
DOI: 10.4064/sm212-2-3
Abstract
An operator T acting on a Banach space X has 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 upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and \sigma (T)=\sigma _{a}(T).
