RT Journal Article
T1 Mazur intersection properties and differentiability of convex functions in Banach spaces
A1 Georgiev, P. G.
A1 Granero, A. S.
A1 Jiménez Sevilla, María del Mar
A1 Moreno, José Pedro
AB 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.
PB London Mathematical Sociey
SN 0024-6107
YR 2000
FD 2000-04
LK https://hdl.handle.net/20.500.14352/58636
UL https://hdl.handle.net/20.500.14352/58636
NO Bulgarian National Foundation for Scientific Investigations
NO DGICYT
DS Docta Complutense
RD 1 may 2024