On generalized property $(v)$ 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 $\sigma (T)=\sigma _{a}(T)$.
