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

Volume 212 / 2012

J. Sanabria, C. Carpintero, E. Rosas, O. García 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 $\sigma (T)=\sigma _{a}(T)$.

Authors

  • J. SanabriaDepartamento de Matemáticas
    Escuela de Ciencias
    Núcleo de Sucre
    Universidad de Oriente
    Cumaná, Venezuela
    e-mail
  • C. CarpinteroDepartamento de Matemáticas
    Escuela de Ciencias
    Núcleo de Sucre
    Universidad de Oriente
    Cumaná, Venezuela
    e-mail
  • E. RosasDepartamento de Matemáticas
    Escuela de Ciencias
    Núcleo de Sucre
    Universidad de Oriente
    Cumaná, Venezuela
    e-mail
  • O. GarcíaDepartamento de Matemáticas
    Escuela de Ciencias
    Núcleo de Sucre
    Universidad de Oriente
    Cumaná, Venezuela
    e-mail

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