On Pelczynski's property (V*) in vector sequence spaces.
On positive operator-valued continuous maps
In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that
On Primary Simplex Spaces.
On projections and unconditional bases in direct sums of Banach spaces II
On projections in spaces of bounded analytic functions with applications
On projections on subspaces of codimension one
On Property β of Rolewicz in Köthe-Bochner Function Spaces
It is proved that the Köthe-Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe-Bochner sequence spaces.
On property (β) of Rolewicz in Köthe-Bochner sequence spaces
We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve...
On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
On regularization in superreflexive Banach spaces by infimal convolution formulas
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex functions converging to f uniformly on bounded sets and...
On Residuality of the Set of Rotund Norms on a Banach Space.
On Reuleaux triangles in Minkowski planes.
On rough norms on Banach spaces
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.