Perturbation Theory for Property (VE) and Tensor Product

Elvis Aponte,José Sanabria,Luis Vásquez

doi:10.3390/math9212775

Abstract

Given a complex Banach space X, we investigate the stable character of the property (VE) 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 (VE) from the tensorial factors T and S to its tensor product.

Highlights

IntroductionAccording to [14], if an operator T satisfies property (VE ), T satisfies equivalently another forty-four spectral properties, among which are Weyl-type theorems such as the properties (VΠ ) and ( gaz) recently studied in [15,16], respectively
We focus our interest on obtaining conditions so that the property (VE ) remains stable under perturbations that are commutative and tensor products for some classes of operators
Some necessary conditions were obtained that guarantee the stable character of property (VE ) under the classic perturbations

Summary

Introduction

According to [14], if an operator T satisfies property (VE ), T satisfies equivalently another forty-four spectral properties, among which are Weyl-type theorems such as the properties (VΠ ) and ( gaz) recently studied in [15,16], respectively. This arouses the interest of studying property (VE ) from different points of view. We focus our interest on obtaining conditions so that the property (VE ) remains stable under perturbations that are commutative and tensor products for some classes of operators

Preliminaries

Conclusions