info:eu-repo/semantics/article
Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
Fecha
2020-01-02Registro en:
Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju; Mazzitelli, Martin Diego; Strong subdifferentiability and local Bishop–Phelps–Bollobás properties; Real Acad Ciencias Exactas Fisicas & Naturales; Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-matematicas; 114; 47; 2-1-2020; 1-16
1578-7303
CONICET Digital
CONICET
Autor
Dantas, Sheldon
Kim, Sun Kwang
Lee, Han Ju
Mazzitelli, Martin Diego
Resumen
Some local versions of the Bishop–Phelps–Bollobás 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< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq 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 ℓ1N×Y.