2023/12/21 by L. Bernal-González, Daniel L. Rodríguez-Vidanes, Bernal-González, Luis +5
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2312.13903
openalex publication_date 2023/12/21 · openalex created_date 2023/12/23 · openalex updated_date 2026/07/28
In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces Λφ,w, equipped with the Luxemburg norm. If a family of Orlicz functions (φn)n=1∞ satisfies certain order relations with respect to a given Orlicz function φ, the subset of the order-continuous subspace (Λφ,w)a whose elements do not belong to \bigcupn=1∞Λφn,w is spaceable, and even maximal-spaceable when φ satisfies the Δ2-condition. We also show that this subset is either residual or empty. In addition, sufficient conditions for this subset not being (α, β)-spaceable are provided. A similar analysis is also performed on the subset Λφ,w ∖ (Λφ,w)a when φ does not satisfy the Δ2-condition. The comparison between different Orlicz-Lorentz spaces is characterized via the generating pairs (φ,w). For a fixed Orlicz function that satisfies the Δ2∞-condition, we provide a characterization of disjointly strictly singular inclusion operators between Orlicz-Lorentz spaces with different weights. As a consequence, there are certain subsets of Orlicz-Lorentz spaces on [0,1] for which lineability problem is not valid. Moreover, various types of (α,β)-lineability and pointwise lineability properties on other nonlinear subsets of Orlicz-Lorentz spaces are examined. These results extend a number of previously known results in Orlicz and Lorentz spaces.