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In this paper, for a bounded linear operator defined on a complex Banach space of infinite dimension, we consider the set of isolated points in its approximate point spectrum, which are eigenvalues of finite multiplicity; this set can be equal to the spectrum of the operator but without its upper semi-Fredholm spectrum, and this relation or equality defines in the literature a new spectral property called the property (ωπ) and is a generalization of the classical a-Weyl theorem. We establish some characterizations and consequences about the property (ωπ), some with topological aspects. Furthermore, we study this property through the Riesz functional calculus. Part of the spectral structure of a linear operator verifying property (ωπ) is described, obtaining some associated properties. [ABSTRACT FROM AUTHOR]

For a bounded linear operator, by local spectral theory methods, we study the property (b z) , which means that the difference of the approximate point spectrum with the upper semi-Fredholm spectrum coincides with the set of all finite-range left poles. We will investigate this property under closed proper subspaces of X , also under the tensor product. In addition, the relationships of this property with other spectral properties are studied. Among others, we will obtain several characterizations for the operators that verify the property (bz) and show that the set of these operators is closed. [ABSTRACT FROM AUTHOR]

In this paper we study the property (gaz) for a bounded linear operator T e L(∊) on a Banach space X, introduced by Zariouh in [Property (gz) for bounded linearoperators, Mat. Vesnik, 65(1) (2013), 94-103], through the methods of local spectral theory. This property is a stronger variant of generalized α-Browder's theorem. In particular, we shall give several characterizations of property (gaz), by using the localized SVEP. [ABSTRACT FROM AUTHOR]

Given a complex Banach space X , we investigate the stable character of the property (V E) for a bounded linear operator T : X → X , under commuting perturbations that are Riesz, compact, algebraic and hereditarily polaroid. We also analyze sufficient conditions that allow the transfer of property (V E) from the tensorial factors T and S to its tensor product. [ABSTRACT FROM AUTHOR]