On singlevaluedness and continuity of monotone mappings
Theory of Frechet cones and nonlinear analysis
On the Clarke’s generalized jacobian
Foreword
On an extension of norms from a subspace to the whole Banach space keeping their rotundity
Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.
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.
Norms that locally depend on countably many linear functionals.
An elementary approach to some questions in higher order smoothness in Banach spaces.
On Residuality of the Set of Rotund Norms on a Banach Space.
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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