EUDML

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.

Pawel Foralewski; Henryk Hudzik — 1997

Collectanea Mathematica

Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm.

Henryk Hudzik; Zenon Zbaszyniak — 1997

Collectanea Mathematica

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.

Henryk Hudzik; Marek Wisla — 1993

Collectanea Mathematica

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.

Yunan Cui; Henryk Hudzik — 1999

Collectanea Mathematica

Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm

Henryk Hudzik; Thomas Landes — 1992

Commentationes Mathematicae Universitatis Carolinae

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 $l^{1}$ and $c_{o}$ in Musielak-Orlicz sequence spaces

Ghassan Alherk; Henryk Hudzik — 1994

Commentationes Mathematicae Universitatis Carolinae

Criteria in order that a Musielak-Orlicz sequence space $l^{Φ}$ contains an isomorphic as well as an isomorphically isometric copy of $l^{1}$ are given. Moreover, it is proved that if $Φ = (Φ_{i})$ , where $Φ_{i}$ are defined on a Banach space, $X$ does not satisfy the $δ_{2}^{o}$ -condition, then the Musielak-Orlicz sequence space $l^{Φ} (X)$ of $X$ -valued sequences contains an almost isometric copy of $c_{o}$ . In the case of $X = I R$ it is proved also that if $l^{Φ}$ contains an isomorphic copy of $c_{o}$ , then $Φ$ does not satisfy the $δ_{2}^{o}$ -condition. These results extend some...