Orlicz function spaces without complemented copies ofl p

This paper proves the existence of Orlicz function spaces Lφ (0, 1) containing no complemented subspaces isomorphic tol ^p for anyp ≠ 2. Some properties of minimal Orlicz function spaces Lφ (0, 1) are also given. Supported in part by CAICYT grant 0338-84.     

Domain representability of certain function spaces

Let Cp(X) be the space of all continuous real-valued functions on a space X, with the topology of pointwise convergence. In this paper we show that Cp(X) is not domain representable unless X is discrete for a class of spaces that includes all pseudo-radial spaces and all generalized ordered spaces. This is a first step toward our conjecture that if X is completely regular, then Cp(X) is domain representable if and only if X is discrete. In addition, we show that if X is completely regular and pseudonormal, then in the function space Cp(X), Oxtoby's pseudocompleteness, strong Choquet completeness, and weak Choquet completeness are all equivalent to the statement “every countable subset of X is closed”.     

Lattice-embeddingL p into Orlicz spaces

Given 0<α≤p≤β<∞, we construct Orlicz function spacesL ^F [0, 1] with Boyd indicesα andβ such thatL ^p is lattice isomorphic to a sublattice ofL ^F [0, 1]. Forp>2 this shows the existence of (non-trivial) separable r.i. spaces on [0, 1] containing an isomorphic copy ofL ^p . The discrete case of Orlicz spaces ℓ ^F (I) containing an isomorphic copy of ℓ ^p (Γ) for uncountable sets Γ ⊂I is also considered. Supported in part by DGICYT, grant PB91-0377.     

On the projection and macphail constants ofl n p spaces

We prove that the projection and Macphail constants ofl _n ^p (1≦p≦2) are asymptotically equivalent ton ^1/2 andn ^−1/2 respectively. We also obtain some relations linking certain parameters of general finite dimensional real Banach spaces. This note is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof. J. Lindenstrauss, to whom the author wishes to express his thanks and appreciation.     

On the unicellularity ofl p (w)

A method of D. V. Yakubovich is sharpened to give extensions of results by him and M. P. Thomas on the right translation-invariant subspace structure for weightedl ^p (Z ⁺) and weightedl ^p (⁺), when the weight tends to 0 at infinity faster than exponentially.     

Upper (lower) monotone coefficient of a point in Orlicz function spaces

The calculation expressions of upper (lower) monotone coefficient of a point in Orlicz function spaces are given.     

Smoothness of the Orlicz norm in Musielak–Orlicz function spaces

In this paper, we present a characterization of support functionals and smooth points in , the Musielak–Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of is also obtained. Some expressions involving the norms of functionals in , the topological dual of , are proved for arbitrary Musielak–Orlicz functions.     

Points of monotonicity in F-normed Orlicz function spaces

Aequationes mathematicae - In this paper points of lower strict monotonicity, upper strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Orlicz function...     

Noncreasy and uniformly noncreasy Orlicz function spaces

We show that in Orlicz function spaces with Orlicz/Luxemburg norm the criteria for being noncreasy and uniformly noncreasy are interesting combinations of conditions.     

On the Baronti constants of Orlicz function spaces

In this paper we calculate the value of the Baronti constants of the Orlicz function spaces equipped with either the Orlicz norm or the gauge norm.     

Pointwise mutipliers of Orlicz function spaces and factorization

In the paper we find representation of the space of pointwise multipliers between two Orlicz function spaces, which appears to be another Orlicz space and the formula for the Young function generating this space is given. Further, we apply this result to find necessary and sufficient conditions for factorization of Orlicz function spaces.     

Polyhedrality in Orlicz spaces

We present a construction of an Orlicz space admitting a C ^∞-smooth bump which depends locally on finitely many coordinates, and which is not isomorphic to a subspace of any C(K), K scattered. In view of the related results this space is possibly not isomorphic to a polyhedral space. Supported by grants: Institutional Research Plan AV0Z10190503, GAČR 201/04/0090, GAČR 201/07/0394, the research project MSM 0021620839, GAČR 201/05/P582.     

Prediction in Orlicz spaces

In this paper, we investigate the prediction (or best approximation) operator from a uniformly convex real Orlicz space to a subset of -lattice measurable functions. In particular, a counterexample to the monotoncity property, which holds in L_p spaces, is given. Also, a sufficient condition for monotonicity to hold is given. Finally, nested -lattices, as occur in isotonic regression, are considered.This author supported by a grant from the Indiana University-Purdue University at Fort Wayne Research and Instructional Development Support Program     

Vector valued double sequence spaces defined by Orlicz function

In this article we introduce some vector valued double sequence spaces defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness etc. and prove some inclusion results.