Uniformly non- Orlicz spaces with Luxemburg norm
On some convexity properties of Orlicz spaces of vector valued functions.
Every nonreflexive Banach lattice has the packaging constant equal to 1/2.
Some class of uniformly non-square Orlicz-Bochner spaces
Uniformly non-ln(1) Musielak-Orlicz Spaces of Bochner Type.
Orlicz spaces which are Lp-spaces. (Summary).
Erratum to the paper "Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm" (Colloq. Math. 65 (1993), 157-164)
Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm
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...
Some basic properties of generalized Calderon-Lozanovskiî.
Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm.
A formula for the distance of an arbitrary element x in Musielak-Orlicz space L^Phi from the subspace E^Phi of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of L^Phi is given for any of these two norms. Criteria for smooth points and smoothness in L^Phi and E^Phi equipped with the Orlicz norm are presented.
On extreme points of Orlicz spaces with Orlicz norm.
In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite which corresponds...
Some geometric properties related to fixed point theory in Cesàro spaces.
Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm
In this paper we extend the result of [6] on the characteristic of convexity of Orlicz spaces to the more general case of Musielak-Orlicz spaces over a non-atomic measure space. Namely, the characteristic of convexity of these spaces is computed whenever the Musielak-Orlicz functions are strictly convex.
Copies of and in Musielak-Orlicz sequence spaces
Criteria in order that a Musielak-Orlicz sequence space contains an isomorphic as well as an isomorphically isometric copy of are given. Moreover, it is proved that if , where are defined on a Banach space, does not satisfy the -condition, then the Musielak-Orlicz sequence space of -valued sequences contains an almost isometric copy of . In the case of it is proved also that if contains an isomorphic copy of , then does not satisfy the -condition. These results extend some...
On some convexities of Orlicz and Orlicz-Bochner spaces
Errata to the paper "Banach-Saks property in some Banach sequence spaces" (Ann. Polon. Math. 65 (1997), 193-202)
Banach-Saks property in some Banach sequence spaces
It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.
On K-nearly uniform convexity in Orlicz spaces.
A generalized projection decomposition in Orlicz-Bochner spaces
In this paper, a precise projection decomposition in reflexive, smooth and strictly convex Orlicz-Bochner spaces is given by the representation of the duality mapping. As an application, a representation of the metric projection operator on a closed hyperplane is presented.
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