Georgiev, P. G.Suárez Granero, AntonioMoreno, José PedroJiménez Sevilla, María Del Mar2023-06-202023-06-202000-04Georgiev, P. G., Suárez Granero, A., Moreno, J. P. & Jiménez Sevilla, M. M. «Mazur Intersection Properties and Differentiability of Convex Functions in Banach Spaces». Journal of the London Mathematical Society, vol. 61, n.o 2, abril de 2000, pp. 531-42. DOI.org (Crossref), https://doi.org/10.1112/S0024610799008625.0024-610710.1112/S0024610799008625https://hdl.handle.net/20.500.14352/58636It 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.journal articlehttps//doi.org/10.1112/S0024610799008625metadata only accessPB 96-0607Álgebra1201 Álgebra