Supereflexive Banach spaces
On some rotundity and smoothness properties of Banach spaces
CONTENTSIntroduction..................................................................................................................................................5Chapter 1. Uniformly rotund directions..................................................................................................7Chapter 2. Duality properties...................................................................................................................15Chapter 4. Some remarks to the theory of weakly uniformly...
Renorming Concerning Mazur's Intersection Property of Balls for Weakly Compact Convex Sets.
Weakly Compact Generating and Shrinking Markusevic Bases
2000 Mathematics Subject Classification: 46B30, 46B03. It is shown that most of the well known classes of nonseparable Banach spaces related to the weakly compact generating can be characterized by elementary properties of the closure of the coefficient space of Markusevic bases for such spaces. In some cases, such property is then shared by all Markusevic bases in the space.
On a Tensor Product Characterization of Nuclearity.
Some notes on Markuševič bases in weakly compactly generated Banach spaces
Projections in dual weakly compactly generated Banach spaces
Gâteaux smooth partitions of unity on weakly compactly generated Banach spaces
Norms that locally depend on countably many linear functionals.
An elementary approach to some questions in higher order smoothness in Banach spaces.
On strongly extreme points
The article contains no abstract
On Residuality of the Set of Rotund Norms on a Banach Space.
Uniformly smooth partitions of unity on superreflexive Banach spaces
Weak compactness and σ-Asplund generated Banach spaces
σ-Asplund generated Banach spaces are used to give new characterizations of subspaces of weakly compactly generated spaces and to prove some results on Radon-Nikodým compacta. We show, typically, that in the framework of weakly Lindelöf determined Banach spaces, subspaces of weakly compactly generated spaces are the same as σ-Asplund generated spaces. For this purpose, we study relationships between quantitative versions of Asplund property, dentability, differentiability, and of weak compactness...
A quantitative version of Krein's theorem.
A quantitative version of Krein's Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly generated Banach spaces are given.
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