arXiv subjects

Henryk Hudzik

Publications and source records attributed to Henryk Hudzik.

3 recordsLinked to original sources

arXiv2022

Quasi-modular spaces with applications to quasi-normed Calderón-Lozanovski\uı spaces

In this paper we introduce the notion of a quasi-modular and we prove that the respective Minkowski functional of the unit quasi-modular ball becomes a quasi-norm. In this way, we refer to and complete the well-known theory related to the notions of a modular and a convex modular that lead to the F-norm and to the norm, respectively. We use the obtained results to consider basic properties of quasi-normed Calderón-Lozanovski\uı spaces $E_φ$, where the lower Matuszewska-Orlicz index $α_φ$ plays the key role. We also give a number of theorems concerning different copies of $l^{\infty}$ in the spaces $E_φ$ in the natural language of suitable properties of the space $E$ and the function $φ$. Our studies are conducted in a full possible generality.

math.FA↗

arXiv2018

Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $\mathbb{R}^{2}$

In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$) studied in [10-11], [14-15] and [20]. Criteria for strict monotonicity, lower and upper local uniform monotonicities and uniform monotonicities of Orlicz spaces and their subspaces of order continuous elements, equipped with these norms, are given in terms of the generating Orlicz functions, and the lattice norm in $\mathbb{R}^{2}$. The problems of strict convexity and of the existence of order almost isometric as well as of order isometric copies in these spaces are also discussed.

math.FA↗

arXiv2006

Basic topological and geometric properties of Cesàro--Orlicz spaces

Necessary and sufficient conditions under which the Cesàro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro--Orlicz spaces $\cfi$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $\cfi$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $\cfi$ are given.

math.FA↗