Perturbation Theory for Property (<i>V</i><i>_E</i>) and Tensor Product

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.

Keywords

• semi-Fredholm operator
• property <i>(V_E)</i>
• commuting perturbations
• tensor product