Convex functions with non-Borel set of Gâteaux differentiability points

Petr Holický; M. Šmídek; Luděk Zajíček

Displaying similar documents to “Convex functions with non-Borel set of Gâteaux differentiability points”

Convex sets in Banach spaces and a problem of Rolewicz

A. Granero, M. Jiménez Sevilla, J. Moreno (1998)

Studia Mathematica

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Let $B_{x}$ be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of $B_{x}$ and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).

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.

Boundaries of convex sets.

M. Valdivia (1993)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Some Applications of Simons’ Inequality

Godefroy, Gilles (2000)

Serdica Mathematical Journal

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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

The controlled separable projection property for Banach spaces

Jesús Ferrer, Marek Wójtowicz (2011)

Open Mathematics

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Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a)...

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

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Let K be a compact Hausdorff space, $C_{p} (K)$ the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and $t_{p} (D)$ the topology in C(K) of pointwise convergence on D. It is proved that when $C_{p} (K)$ is Lindelöf the $t_{p} (D)$ -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and $C_{p} (K)$ is Lindelöf, then K is metrizable if, and only if, there is a countable...

Strong subdifferentiability of norms and geometry of Banach spaces

Gilles Godefroy, Vicente Montesinos, Václav Zizler (1995)

Commentationes Mathematicae Universitatis Carolinae

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The strong subdifferentiability of norms (i.eȯne-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.