Relatively uniformly continuous semigroups on vector lattices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Kandic, M.^1,2  Kaplin, M.^1,2 

[1] Univ Ljubljana, Fac Math & Phys, Jadranska 19, SI-1000 Ljubljana, Slovenia

[2] Inst Math Phys & Mech, Jadranska 19, SI-1000 Ljubljana, Slovenia

关键词: Vector lattices;    Relatively uniform convergence;    Relatively uniform topology;    Relatively uniform continuity;    Strongly continuous semigroups;   

DOI  :  10.1016/j.jmaa.2020.124139

来源: Elsevier

【 摘 要 】

In this paper we introduce the notions of relatively uniform continuity and strong continuity with respect to the relatively uniform topology for semigroups on general vector lattices. These notions allow us to study semigroups on non-locally convex spaces such as L-p(R) for 0 < p < 1 and non-complete spaces such as Lip(R), UC(R), and C-c(R). We provide examples of relatively uniform continuous semigroups such as the ( left) translation semigroup and the Ornstein-Uhlenbeck semigroup. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free