Currently displaying 1 – 16 of 16

Showing per page

Order by Relevance | Title | Year of publication

Boundary of polyhedral spaces: an alternative proof.

Libor Vesely — 2000

Extracta Mathematicae

A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space...

Chebyshev centers in hyperplanes of c 0

Libor Veselý — 2002

Czechoslovak Mathematical Journal

We give a full characterization of the closed one-codimensional subspaces of c 0 , in which every bounded set has a Chebyshev center. It turns out that one can consider equivalently only finite sets (even only three-point sets) in our case, but not in general. Such hyperplanes are exactly those which are either proximinal or norm-one complemented.

For a dense set of equivalent norms, a non-reflexive Banach space contains a triangle with no Chebyshev center

Libor Veselý — 2001

Commentationes Mathematicae Universitatis Carolinae

Let X be a non-reflexive real Banach space. Then for each norm | · | from a dense set of equivalent norms on X (in the metric of uniform convergence on the unit ball of X ), there exists a three-point set that has no Chebyshev center in ( X , | · | ) . This result strengthens theorems by Davis and Johnson, van Dulst and Singer, and Konyagin.

The distance between subdifferentials in the terms of functions

Libor Veselý — 1993

Commentationes Mathematicae Universitatis Carolinae

For convex continuous functions f , g defined respectively in neighborhoods of points x , y in a normed linear space, a formula for the distance between f ( x ) and g ( y ) in terms of f , g (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...

On vector functions of bounded convexity

Libor VeselýLuděk Zajíček — 2008

Mathematica Bohemica

Let X be a normed linear space. We investigate properties of vector functions F : [ a , b ] X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K a b F is equal to the variation of F + ' on [ a , b ) . As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.

Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces

Victor KleeLibor VeselýClemente Zanco — 1996

Studia Mathematica

For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...

Page 1

Download Results (CSV)