Class Of Orlicz Spaces Research Articles

Disjointly homogeneous Orlicz spaces revisited

Let \(1 \le p \le \infty \). A Banach lattice X is said to be p-disjointly homogeneous or \((p-DH)\) (resp. restricted \((p-DH)\)) if every normalized disjoint sequence in X (resp. every normalized sequence of characteristic functions of disjoint subsets) contains a subsequence equivalent in X to the unit vector basis of \(\ell _p\). We revisit DH-properties of Orlicz spaces and refine some previous results of this topic, showing that the \((p-DH)\)-property is not stable under duality in the class of Orlicz spaces and the classes of restricted \((p-DH)\) and \((p-DH)\) Orlicz spaces are different. Moreover, we give a characterization of uniform \((p-DH)\) Orlicz spaces and establish also closed connections between this property and the duality of the DH-property.

An operator ideal generated by Orlicz spaces

Absolutely varphi -summing operators between Banach spaces generated by Orlicz spaces are investigated. A variant of Pietsch’s domination theorem is proved for these operators and applied to prove vector-valued inequalities. These results are used to prove asymptotic estimates of pi _varphi -summing norms of finite-dimensional operators and also diagonal operators between Banach sequence lattices for a wide class of Orlicz spaces based on exponential convex functions varphi . The key here is the description of a space of coefficients of the Rademacher series in this class of Orlicz spaces, proved via interpolation methods. As by-product, some absolutely varphi -summing operators on the Hilbert space ell _2 are characterized in terms of its approximation numbers.

Extension of the Best Constant Approximation Operator in Orlicz Spaces

In this article we deal with the best -approximation operator by constants extended from an Orlicz space to the space where denotes the right derivative of the function We obtain pointwise convergence for a suitable class of functions. Also we consider a maximal operator which allows as to get modular convergence for a specific class of Orlicz spaces.

Distributions with Heavy Tails in Orlicz Spaces

This paper relies on the application of Kantorovich functionals on quasi-interior points of the positive cone for certain classes of Orlicz spaces. Particularly we provide the asymptotic calculation of the ruin probability in the renewal risk model under heavy-tailed claims in the Orlicz spaces. This application assures the extension of classical asymptotic theory of regular variation.

A constructive approach to the duality theorem for certain Orlicz spaces

One of the intriguing complications of constructive analysis is that it does not seem possible to obtain examples of inseparable Banach spaces; more precisely, when one comes to study explicit examples one finds that one cannot assign a constructively denned norm to every vector in the space. One of the objectives of (2) was to make a detailed study of an explicit class of Banach spaces, containing both separable and inseparable examples, in the hope that one might begin better to understand these matters. We chose for this study the class of Orlicz spaces, primarily because the simplest examples (namely the Lebesgue spaces LP) had already been the objective of detailed constructive work in (1).

Rotundity of Orlicz Spaces

Rotund Orlicz spaces and Orlicz spaces that contain isomorphic copies of l∘ and co are characterized in the class of Orlicz spaces over measure spaces that are not purely atomic.