Norm attaining operators and variational principle

Abstract

. We establish a linear variational principle extending Deville–Godefroy– Zizler’s one. We use this variational principle to prove that if X is a Banach space having property ( α ) of Schachermayer and Y is any Banach space, then the set of all strongly norm attaining linear operators from X into Y is the complement of a σ -porous set. Moreover, we apply our results to an abstract class of (linear and nonlinear) operator spaces.