On the differentiation of convex functions
On the distance between two Chebyshev sets in Banach spaces.
On the distribution of the norm for a gaussian measure
On the equality of injective and projective tensor products
On the exact value of Jung constants of Orlicz sequence spaces.
On the existence of almost greedy bases in Banach spaces
We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an...
On the extension of rotund norms.
On the Extreme Points and Strongly Extreme Points in Köther-Bochner Spaces
On the Facial Structure of the Unit Ball of a GM-Space.
On the fixed point property in direct sums of Banach spaces with strictly monotone norms
It is shown that if a Banach space X has the weak Banach-Saks property and the weak fixed point property for nonexpansive mappings and Y has the asymptotic (P) property (which is weaker than the condition WCS(Y) > 1), then X ⊕ Y endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if X admits a 1-unconditional basis.
On the fixed points of nonexpansive mappings in direct sums of Banach spaces
We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
On the fixed-point property of unital uniformly closed subalgebras of .
On the frame of the unit ball of Banach spaces
The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit balls of...
On the Fréchet differentiability of distance functions
On the geometry of Banach spaces with modulus of convexity of power type 2
We use one-dimensional differential inequalities to estimate the squareness and type of Banach spaces with modulus of convexity of power type two. The estimates obtained are sharp and the constants involved moderate.
On the geometry of spaces of K-valued operators
On the global stable manifold
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in the general Banach setting gives rise to subtle questions about the possibility of extending germs of diffeomorphisms.
On the -property of some Banach sequence spaces
In this paper we define a generalized Cesàro sequence space and consider it equipped with the Luxemburg norm under which it is a Banach space, and we show that the space posses property (H) and property (G), and it is rotund, where is a bounded sequence of positive real numbers with for all .
On the H-property and rotundity of Cesàro direct sums of Banach spaces
In this paper, we define the direct sum of Banach spaces X₁,X₂,..., and Xₙ and consider it equipped with the Cesàro p-norm when 1 ≤ p < ∞. We show that has the H-property if and only if each has the H-property, and has the Schur property if and only if each has the Schur property. Moreover, we also show that is rotund if and only if each is rotund.
On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm
Boulahia and the present authors introduced the Orlicz norm in the class -a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.