Rotundity and monotonicity properties of selected Cesàro function spaces

• Published in: Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 22; no. 1; pp. 357 - 377
• Main Authors: Kiwerski, Tomasz, Kolwicz, Paweł
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2018; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Continuity (mathematics); Econometrics; Events planning; Fourier Analysis; Function space; Mathematics; Mathematics and Statistics; Meetings; Operator Theory; Potential Theory; Monotonicity properties; 46A80; Cesàro–Lorentz function space; 46B04; Cesàro function space; Order continuity; 46E30; 46B20; 46B42; Cesàro–Orlicz function space; Cesàro–Marcinkiewicz function space; Rotundity
• ISSN: 1385-1292; 1572-9281
• DOI: 10.1007/s11117-017-0515-8

We study rotundity, strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity in some classes of Cesàro function spaces. We present full criteria of these properties in the Cesà ro–Orlicz function spaces C e s φ (under some mild assumptions on the Orlicz function φ ). Next, we prove a characterization of strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity in the Cesàro–Lorentz function spaces C Λ ϕ . We also show that the space C Λ ϕ is never rotund. Finally, we will prove that Cesàro–Marcinkiewicz function space C M ϕ ( ∗ ) is neither strictly monotone nor order continuous for any quasi-concave function ϕ .