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On weak Hadamard differentiability of convex functions on Banach spaces. (English) Zbl 0886.46050
Summary: We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to \(\ell_1\).

46G05 Derivatives of functions in infinite-dimensional spaces
46B20 Geometry and structure of normed linear spaces
46A17 Bornologies and related structures; Mackey convergence, etc.
46A03 General theory of locally convex spaces
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
46B25 Classical Banach spaces in the general theory
Full Text: DOI
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