Person:
Suárez Granero, Antonio

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First Name
Antonio
Last Name
Suárez Granero
URI
https://hdl.handle.net/20.500.14352/75701
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Análisis Matemático Matemática Aplicada
Area
Análisis Matemático
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Item Type: Publication × Subject: PB 96-0607 ×

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    Mazur intersection properties and differentiability of convex functions in Banach spaces
    (Journal of the London Mathematical Society, 2000) Georgiev, P. G.; Suárez Granero, Antonio; Moreno, José Pedro; Jiménez Sevilla, María Del Mar
    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.