On new strong versions of Browder type theorems

An operator T acting on a Banach space X satisfies the property ( UW Π ) if σ a ( T )∖ σ S F + − $\begin{array}{} \sigma_{SF_{+}^{-}} \end{array} $ ( T ) = Π ( T ), where σ a ( T ) is the approximate point spectrum of T , σ S F + − $\begin{array}{} \sigma_{SF_{+}^{-}} \end{array} $ ( T ) is the upper semi-Weyl spectrum of T and Π ( T ) the set of all poles of T . In this paper we introduce and study two new spectral properties, namely ( V Π ) and ( V Π a ), in connection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we have that T satisfies property ( V Π ) if and only if T satisfies property ( UW Π ) and σ ( T ) = σ a ( T ).

Abstract licence: CC BY-NC-ND

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