On the lattice structure of invariant functions for Markov operators on
In the paper, a sufficient and necessary condition is given for the locally uniformly weak star rotundity of Orlicz spaces with Orlicz norms.
Si dimostra che il funzionale è semicontinuo inferiormente su , rispetto alla topologia indotta da , qualora l’integrando sia una funzione non-negativa, misurabile in , convessa in , limitata nell’intorno dei punti del tipo , e tale che la funzione sia semicontinua inferiormente su .
In this article, we investigate new topological descriptions for two well-known mappings and defined on intermediate rings of . Using this, coincidence of each two classes of -ideals, -ideals and -ideals of is studied. Moreover, we answer five questions concerning the mapping raised in [J. Sack, S. Watson, and among intermediate rings, Topology Proc. 43 (2014), 69–82].
Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for where ℝ is the reals.
Let L(Φ) [0, +∞) be the Orlicz function space generated by N-function Φ(u) with Luxemburg norm. We show the exact nonsquare constant of it when the right derivative φ(t) of Φ(u) is convex or concave.