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Título:
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Mazur intersection properties and differentiability of convex functions in Banach spaces
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Autores:
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Georgiev, P. G. ;
Granero, A. S. ;
Jiménez Sevilla, María del Mar ;
Moreno, José Pedro
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Tipo de documento:
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texto impreso
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Editorial:
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London Mathematical Sociey, 2000-04
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Álgebra
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Tipo = Artículo
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Resumen:
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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(?) and [script l][infty infinity](?) are Fréchet differentiable on a dense G? 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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