Journal of Convex Analysis 28 (2021), No. 4, 1087--1096
Copyright Heldermann Verlag 2021
Structure of Sets of Strong Subdifferentiability in Dual L1-Spaces
C. R. Jayanarayanan
Department of Mathematics, Indian Institute of Technology, Palakkad, India
crjayan@iitpkd.ac.in
T. S. S. R. K. Rao
Department of Mathematics, Ashoka University, Sonipat, India
srin@fulbrightmail.org
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.
Keywords: Strong subdifferentiability, strong proximinality, M-ideals, L-1-predual space.
MSC: 41A65; 46B20, 41A50, 46E15.
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