The superposition operator in Musielak-Orlicz spaces of vector-valued functions
Continuity of superposition operators on and
On non-solid Köthe space of type
Some geometric properties in Orlicz sequence spaces equipped with Orlicz norm.
P-convexity of Musielak-Orlicz sequence spaces of Bochner type.
Metric projections and best approximants in Bochner-Orlicz spaces.
In the first section of this paper there are given criteria for strict convexity and smoothness of the Bochner-Orlicz space with the Orlicz norm as well as the Luxemburg norm. In the second one that geometrical properties are applied to the characterization of metric projections and zero mean valued best approximants to Bochner-Orlicz spaces.
P-convexity of Musielak-Orlicz function spaces of Bochner type.
It is proved that the Musielak-Orlicz function space LF(mu,X) of Bochner type is P-convex if and only if both spaces LF(mu,R) and X are P-convex. In particular, the Lebesgue-Bochner space Lp(mu,X) is P-convex iff X is P-convex.
A strongly extreme point need not be a denting point in Orlicz spaces equipped with the Orlicz norm
There are necessary conditions for a point x from the unit sphere to be a denting point of the unit ball of Orlicz spaces equipped with the Orlicz norm generated by arbitrary Orlicz functions. In contrast to results in [12, 17, 16], we present also examples of Orlicz spaces in which strongly extreme points of the unit ball are not denting points.
Modulus of dentability in
We introduce the notion of the modulus of dentability defined for any point of the unit sphere S(X) of a Banach space X. We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of is a LUR-point. Consequently, the set of LUR-points of the unit ball of is empty.
Uniform -property in
On -convex Musielak-Orlicz spaces
In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is -convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16].
Linear functionals on some non-locally convex generalized Orlicz 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.
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.
A note on strict K-monotonicity of some symmetric function spaces
We discuss some sufficient and necessary conditions for strict K-monotonicity of some important concrete symmetric spaces. The criterion for strict monotonicity of the Lorentz space with
Weak orthogonality and weak property () in some Banach sequence spaces
It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property () in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.
Differentiability of Musielak-Orlicz sequence spaces
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