%0 Journal Article
%A Georgiev, P. G.
%A Granero, A. S.
%A Jiménez Sevilla, María del Mar
%A Moreno, José Pedro
%T Mazur intersection properties and differentiability of convex functions in Banach spaces
%D 2000
%@ 0024-6107
%U https://hdl.handle.net/20.500.14352/58636
%X It is proved that the dual of a Banach space with the Mazur intersection property is almost weak* Asplund. Analogously, the predual of a dual space with the weak* Mazur intersection property is almost Asplund. Through the use of these arguments, it is found that, in particular, almost all (in the Baire sense) equivalent norms on [script l]1(Γ) and [script l][infty infinity](Γ) are Fréchet differentiable on a dense Gδ subset. Necessary conditions for Mazur intersection properties in terms of convex sets satisfying a Krein–Milman type condition are also discussed. It is also shown that, if a Banach space has the Mazur intersection property, then every subspace of countable codimension can be equivalently renormed to satisfy this property.
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