Intersections of closed balls and geometry of Banach spaces



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Granero, A. S. and Jiménez Sevilla, María del Mar and Moreno, José Pedro (2004) Intersections of closed balls and geometry of Banach spaces. Extracta Mathematicae, 19 (1). pp. 55-92. ISSN 0213-8743

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In section 1 we present definitions and basic results concerning the Mazur intersection property (MIP) and some of its related properties as the MIP* . Section 2 is devoted to renorming Banach spaces with MIP and MIP*. Section 3 deals with the connections between MIP, MIP* and differentiability of convex functions. In particular, we will focuss on Asplund and almost Asplund spaces. In Section 4 we discuss the interplay between porosity and MIP. Finally, in section 5 we are concerned with the stability of the (closure of the) sum of convex sets which are intersections of balls and
with Mazur spaces.

Item Type:Article
Uncontrolled Keywords:Convex bodies, Binary intersection property, Mazur sets, Mazur spaces, Mazur intersection property, Polyhedral norms, Stonean compact spaces, Porosity.
Subjects:Sciences > Mathematics > Algebra
ID Code:22087
Deposited On:26 Jun 2013 17:52
Last Modified:21 Jun 2018 10:55

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