A generalization of the Zariouh's property (gaz) through local spectral theory

Resumen

In this work, we present for the first time an in-depth study of the relationship between the upper semi-B-Fredholm spectrum and the left Drazin spectrum. This connection leads to the definition of a new spectral property, denoted as (ggaz), which generalizes the previously studied property (gaz). Through the framework of local spectral theory, we derive several characterizations of operators that satisfy the (ggaz) property. Moreover, we demonstrate that the set of operators fulfilling this property constitutes a Banach space, highlighting the structural significance of (ggaz) in operator theory.
Key words: Property (gaz), Property (ggaz), semi-B-Fredholm operator, Left-Drazin Operator, SVEP..