Strong subdifferentiability and local Bishop-Phelps-Bollobas properties

Abstract

Some local versions of the Bishop-Phelps-Bollobas property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304-323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2<p,q<infinity, the norm of the projective tensor product lp circle times<^></mml:mover>pi lq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on l(1)(N)xY.