Geodesic
Structure of Sets of Strong Subdifferentiability in Dual L1-Spaces
Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1087-1096
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We analyse the structure of finite dimensional subspaces of the set of points of strong subdifferentiability in a dual space. In a dual L1(μ) space, such a subspace is in the discrete part of the Yoshida-Hewitt type decomposition. In this set up, any Banach space consisting of points of strong subdifferentiability is necessarily finite dimensional. Our results also lead to streamlined and new proofs of results from the study of strong proximinality for subspaces of finite co-dimension in a Banach space.
Classification : 41A65, 46B20, 41A50, 46E15
Mots-clés : Strong subdifferentiability, strong proximinality, M-ideals, L-1-predual space 
@article{JCA_2021_28_4_JCA_2021_28_4_a4,
     author = {C. R. Jayanarayanan and T. S. S. R. K. Rao},
     title = {Structure of {Sets} of {Strong} {Subdifferentiability} in {Dual} {L\protect\textsuperscript{1}-Spaces}},
     journal = {Journal of convex analysis},
     pages = {1087--1096},
     year = {2021},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a4/}
}
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C. R. Jayanarayanan; T. S. S. R. K. Rao. Structure of Sets of Strong Subdifferentiability in Dual L1-Spaces. Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1087-1096. http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a4/