2019/05/21 by Dantas, Sheldon, Kim, Sun Kwang, Lee, Han Ju +1
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1905.08483
It has been recently presented some local versions of the Bishop-Phelps-Bollobás type property for operators. In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of the Bishop-Phelps-Bollobás type results for multilinear mappings, and also provide some interesting examples which shows that this study is not just a mere generalization of the linear case. We study those properties for bilinear forms on ℓp × ℓq using the strong subdifferentiability of the norm of the Banach space ℓp ⊗π ℓq. 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.