Stability in Banach spaces.
Stability in vector valued -spaces
Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces
* 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...
Stable Banach spaces
Stable points of unit ball in Orlicz spaces
The aim of this paper is to investigate stability of unit ball in Orlicz spaces, endowed with the Luxemburg norm, from the “local” point of view. Firstly, those points of the unit ball are characterized which are stable, i.e., at which the map is lower-semicontinuous. Then the main theorem is established: An Orlicz space has stable unit ball if and only if either is finite dimensional or it is isometric to or satisfies the condition or (appropriate to the measure and the function...
Stable smooth and extreme points, and reflexivity
Starlike bodies and deleting diffeomorphisms in Banach spaces.
Strict u-ideals in Banach spaces
We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c₀. We also show that is not a u-ideal.
Strictly convex spheres in V-spaces
Strong monotonicity and Lipschitz-continuity of the duality mapping
Strong proximinality and polyhedral spaces.
In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.
Strong subdifferentiability of norms and geometry of Banach spaces
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.
Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm
A criterion for strongly exposed points of the unit ball in Musielak-Orlicz sequence spaces equipped with Orlicz norm is given.
Strongly Extreme Points in Banach Spaces.
Strongly nonnorming subspaces and prequojections
Strongly proximinal subspaces of finite codimension in C(K)
We characterize strongly proximinal subspaces of finite codimension in C(K) spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in C(K) is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of C(K).
Structural properties of operator spaces
Subspace mixing properties of operators in with applications to Gluskin spaces
Subspaces of , p > 2, determined by partitions and weights
Many of the known complemented subspaces of have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of many well known complemented subspaces of . It is proved that the class of spaces with such norms is stable under (p,2) sums. By introducing the notion of an envelope norm, we obtain a necessary condition for a Banach sequence space with norm given by partitions...
Subspaces of which do not contain -isomorphically