On generalized property $(v)$ for bounded linear operators

J. Sanabria ¹   ; C. Carpintero ¹   ; E. Rosas ¹   ; O. García ¹

¹ Departamento de Matemáticas Escuela de Ciencias Núcleo de Sucre Universidad de Oriente Cumaná, Venezuela

Studia Mathematica, Tome 212 (2012) no. 2, pp. 141-154

Résumé

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 $\sigma (T)=\sigma _{a}(T)$.

Détail

DOI : 10.4064/sm212-2-3

Keywords: operator acting banach space has property sigma setminus sigma sbf where sigma approximate point spectrum sigma sbf upper semi b weyl spectrum set isolated eigenvalues nbsp introduce study spectral properties connection weyl type theorems among other results satisfies only satisfies sigma sigma