Norm attaining operators and variational principle
Tom 265 / 2022
Studia Mathematica 265 (2022), 343-360
MSC: Primary 46B20, 47L05, 28A05; Secondary 47B48, 26A21.
DOI: 10.4064/sm210628-6-9
Opublikowany online: 4 March 2022
Streszczenie
We establish a linear variational principle extending Deville–Godefroy–Zizler’s one. We use this variational principle to prove that if is a Banach space having property (\alpha ) 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 \sigma -porous set. Moreover, we apply our results to an abstract class of (linear and nonlinear) operator spaces.
