Rotundity and monotonicity properties of selected Cesàro function spaces

Abstract

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 Ces 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 φ . We also show that the space C 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 quasiconcave function φ.

Quotients, $$\ell _\infty $$ and abstract Cesàro spaces

“…This result implies immediate applications for the Köthe-Bochner spaces and the Cesàro-Orlicz spaces (cf. [43] for a more direct approach in the case of different types of the Cesàro function spaces); (c) Mastyło in [58] and [59] investigated some structural properties of the space D X (S).…”

Quotients, $\ell_\infty$ and abstract Cesàro spaces

“…This result implies immediate applications for the Köthe-Bochner spaces and the Cesàro-Orlicz spaces, cf. [KK18a] for a more direct approach in the case of different types of the Cesàro function spaces; (c) Mastyło in [Mas91] and [Mas92] investigated some structural properties of the space D E (S).…”

Local monotonicity coefficients in Orlicz sequence spaces equipped with the p-Amemiya norm

“…For lattice theory and monotonicity results in some Banach lattices we refer to [5][6][7][8][9][10][11][12][13][14]. Monotonicity has been extensively studied by several researchers in some specific lattices such as Lorentz, Orlicz or Musielak-Orlicz spaces [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”