Study of the property (bz) using local spectral theory methods

Abstract

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.