2022/08/18 by Paweł Foralewski, Foralewski, Paweł, Henryk Hudzik +3 · 1 citation
Computer Science · Mathematics · #46A16 #46A80 #46B20 #46E30 #Analytic and geometric function theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2208.08970
openalex publication_date 2022/08/18 · openalex created_date 2022/08/20 · openalex updated_date 2026/07/28
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 Eφ, where the lower Matuszewska-Orlicz index αφ plays the key role. We also give a number of theorems concerning different copies of l∞ in the spaces Eφ in the natural language of suitable properties of the space E and the function φ. Our studies are conducted in a full possible generality.