Displaying similar documents to “Dual spaces generated by the interior of the set of norm attaining functionals”

Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. ...

Complex Banach spaces with Valdivia dual unit ball.

Ondrej F. K. Kalenda (2005)

Extracta Mathematicae

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We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.

On nested sequences of convex sets in Banach spaces

Jesús M. F. Castillo, Manuel González, Pier Luigi Papini (2014)

Studia Mathematica

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We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.

Characterizations of almost transitive superreflexive Banach spaces

Julio Becerra Guerrero, Angel Rodriguez Palacios (2001)

Commentationes Mathematicae Universitatis Carolinae

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Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the unit sphere of X , we have lim sup ∥ h ∥ → 0 ∥ u + h ∥ + ∥ u - h ∥ - 2 ∥ h ∥ = 2 . We note that, in general, the property of convex transitivity for...