TY - JOUR
T1 - Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
AU - Dantas, Sheldon
AU - Kim, Sun Kwang
AU - Lee, Han Ju
AU - Mazzitelli, Martin
N1 - Publisher Copyright:
© 2020, The Royal Academy of Sciences, Madrid.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - 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.
AB - 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.
KW - Banach space
KW - Bishop–Phelps–Bollobás property
KW - Norm attaining operators
UR - http://www.scopus.com/inward/record.url?scp=85077216964&partnerID=8YFLogxK
U2 - 10.1007/s13398-019-00741-1
DO - 10.1007/s13398-019-00741-1
M3 - Article
AN - SCOPUS:85077216964
SN - 1578-7303
VL - 114
JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
IS - 2
M1 - 47
ER -