Georgiev, P. G.Granero, A. S.Jiménez Sevilla, María del MarMoreno, José Pedro2023-06-202023-06-202000-040024-610710.1112/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 articlehttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=53605http://journals.cambridge.org/action/login?sessionId=9FC94AB168D166077F09F52784BE1229.journalsmetadata only accessPB 96-0607Álgebra1201 Álgebra