We show that n-dimensional spaces with maximal projection constants exist not only as subspaces of but also as subspaces of l₁. They are characterized by a rigid set of vector conditions. Nevertheless, we show that, in general, there are many non-isometric spaces with maximal projection constants. Several examples are discussed in detail.
Nachdem der Begriff des sphärischen Bildes der Menge und der Begriff von sphärisch äquivalenten Mengen eingeführt wurde, werden verschiedene Zusammenhänge zwischen der Menge und ihrem sphärischen Bild untersucht und zwar unter verschiedenen Voraussetzung über (z. B. ihre Beschränkheit, Unbeschränkheit, strenge Konvexität). Die bewiesene Tatsache, dass die Menge und ihre -Umgebung sphärisch äquivalent sind, kann - sowie andere Ergebnisse der Arbeit - in der Theorie der konvexen parametrischen...
The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set in a topological vector space is stable if the midpoint map , is open with respect to the inherited topology in . The main theorem is established: In the Orlicz space the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.
* This work was supported by the CNR while the author was visiting the University of Milan.To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function and of its conjugate...
The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.
The paper presents a short survey of stereological problems concerning dihedral angles, their solutions and applications, and introduces a graph for determining the distribution functions of planar angles under the hypothesis that dihedral angles in are of the same size and create a random field.
Precipitates modelled by rotary symmetrical lens-shaped discs are situated on matrix grain boundaries and the homogeneous specimen is intersected by a plate section. The stereological model presented enables one to express all basic parameters of spatial structure and moments of the corresponding probability distributions of quantitative characteristics of precipitates in terms of planar structure parameters the values of which can be estimated from measurements carried out in the plane section....