2018/05/17 by Yunan Cui, Cui, Yunan, Henryk Hudzik +3
Computer Science · Mathematics · #46A80 #46B20 #46B42 #46B45 #46E30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1805.06720
openalex publication_date 2018/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in ℝ2 are defined and studied. This family of norms includes the family of the p-Amemiya norms (1≤ p≤∞) 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 ℝ2. 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.