On semi-uniform Kadec-Klee Banach spaces.
On Some Classes of Operators on C(K,X)
Suppose X and Y are Banach spaces, K is a compact Hausdorff space, Σ is the σ-algebra of Borel subsets of K, C(K,X) is the Banach space of all continuous X-valued functions (with the supremum norm), and T:C(K,X) → Y is a strongly bounded operator with representing measure m:Σ → L(X,Y). We show that if T is a strongly bounded operator and T̂:B(K,X) → Y is its extension, then T is limited if and only if its extension T̂ is limited, and that T* is completely continuous (resp. unconditionally...
On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm
In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions endowed with the Luxemburg norm.
On some convexity properties of generalized Cesàro sequence spaces.
On some convexity properties of Musielak-Orlicz spaces
On some convexity properties of Orlicz spaces of vector valued functions.
On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, -property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.
On some geometric constants and the fixed point property for multivalued nonexpansive mappings.
On some geometric properties concerning closed convex sets.
In this article, we consider the (weak) drop property, weak property (a), and property (w) for closed convex sets. Here we give some relations between those properties. Particularly, we prove that C has (weak) property (a) if and only if the subdifferential mapping of Cº is (n-n) (respectively, (n-w)) upper semicontinuous and (weak) compact valued. This gives an extension of a theorem of Giles and the first author.
On some geometric properties in C(K,X) and C(K,X)*.
On some geometric properties of certain Köthe sequence spaces
It is proved that if a Kothe sequence space is monotone complete and has the weakly convergent sequence coefficient WCS, then is order continuous. It is shown that a weakly sequentially complete Kothe sequence space is compactly locally uniformly rotund if and only if the norm in is equi-absolutely continuous. The dual of the product space of a sequence of Banach spaces , which is built by using an Orlicz function satisfying the -condition, is computed isometrically (i.e. the exact...
On some global and local geometric properties of Calderón-Lozanovskiĭ spaces
Criteria for full k-rotundity (k ∈ ℕ, k ≥ 2) and uniform rotundity in every direction of Calderón-Lozanovskiĭ spaces are formulated. A characterization of -points in these spaces is also given.
On some local geometry of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm
Criteria for strong U-points, compactly locally uniformly rotund points, weakly compactly locally uniformly rotund points and locally uniformly rotund points in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm are given.
On some parameters associated with normed lattices and on series characterization of M-spaces
On some properties for dual spaces of Musielak-Orlicz function spaces
We will present relationships between the modular ρ* and the norm in the dual spaces in the case when a Musielak-Orlicz space is equipped with the Orlicz norm. Moreover, criteria for extreme points of the unit sphere of the dual space will be presented.
On some subsets of
On spaces with local unconditional structure
On spreading -sequences in Banach spaces
We introduce and study the spreading-(s) and the spreading-(u) property of a Banach space and their relations. A space has the spreading-(s) property if every normalized weakly null sequence has a subsequence with a spreading model equivalent to the usual basis of ; while it has the spreading-(u) property if every weak Cauchy and non-weakly convergent sequence has a convex block subsequence with a spreading model equivalent to the summing basis of . The main results proved are the following: (a)...
On spreading models in
On strictly convex and strictly 2-convex 2-normed spaces. II.