Abstract
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 Lp(R) for 0<p<1 and non-complete spaces such as Lip(R), UC(R), and Cc(R). We provide examples of relatively uniform continuous semigroups such as the (left) translation semigroup and the Ornstein-Uhlenbeck semigroup.
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