Onl p-complemented copies in Orlicz spaces

Let 1<α≦β<∞ andF be an arbitrary closed subset of the interval [α,β]. An Orlicz sequence spacel ^φ (resp. an Orlicz function spaceL ^φ(μ)) with associated indices α and β is found in such a way that the set of valuesp for which thel ^p-space is isomorphic to a complemented subspace ofl ^φ (resp.L ^φ(μ)) is precisely the given setF (resp.F ∪ {2}). Also, a recent result of Hernández and Peirats [1] is extended showing that, even for the case in which the indices satisfy α_φ ^∞<2<β_φ ^∞, there exist minimal Orlicz function spacesL ^φ(μ) with no complemented copy ofl ^p for anyp ≠ 2. Supported in part by CAICYT grant 0338-84.     

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.     

On Orlicz sequence spaces. II

Given a separable Orlicz sequence spacel _F we investigate those Orlicz sequence spacesl _f which are isomorphic to subspaces (respectively complemented subspaces) ofl _F. We give in particular an example of a reflexive Orlicz sequence space which does not contain anyl _p, 1<p<∞, as a complemented subspace.     

Onl p -copies in Musielak-Orlicz sequence spaces

The authors would like to thank Francisco L. Hernández for some friendly and interesting discussions on this paper.     

Noncommutative Orlicz spaces associated to a state II

We introduce and study the noncommutative Orlicz spaces associated to a normal faithful state on a semifinite von Neumann algebra. We also prove some convergence theorems for the (unbounded) trace measurable operators.     

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     

Hardy inequalities in Orlicz spaces

We establish a sharp extension, in the framework of Orlicz spaces, of the (-dimensional) Hardy inequality, involving functions defined on a domain , their gradients and the distance function from the boundary of .

     

Analytic norms in Orlicz spaces

It is shown that an Orlicz sequence space admits an equivalent analytic renorming if and only if it is either isomorphic to or isomorphically polyhedral. As a consequence, we show that there exists a separable Banach space admitting an equivalent -Fréchet norm, but no equivalent analytic norm.

     

Lattice-universal Orlicz spaces on probability spaces

Lattice-universal Orlicz function spacesL ^F _α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL ^F _α,β[0, 1] with indices α and β such that every Orlicz function spaceL ^G [0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL ^F _α,β[0, 1]. The existence of classes of universal Orlicz spacesl ^Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case. Partially supported by BFM2001-1284.     

Random elements in Orlicz spaces

We give sufficient conditions for random elements of L₁(T, , ) to belong to L(T, Ol,) the Orlicz space.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 127–132, 1987.     

Approximation in weighted Orlicz spaces

We prove some direct and converse theorems of trigonometric approximation in weighted Orlicz spaces with weights satisfying so called Muckenhoupt’s A _p condition.     

On approximation in Weighted Orlicz spaces

An inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.