Relatively uniformly continuous semigroups of positive operators on vector latticesKaplin, Michael (Avtor) Kramar Fijavž, Marjeta (Mentor) Kandić, Marko (Komentor) vector latticesrelatively uniform convergencerelatively uniform topologyrelatively uniform continuitypositive operator semigroupsstrongly continuous semigroupsHille-Yosida theoremIn this thesis we introduce and study notions of relatively uniform continuity and strong continuity with respect to the relatively uniform topology for semigroups of operators on general vector lattices. These notions allow us to study semigroups on non-locally convex spaces, such as $L^p({\mathbb R})$ for $0 < p < 1$, and non-complete spaces, such as ${\rm Lip}({\mathbb R})$, ${\rm UC}({\mathbb R})$, and ${\rm C}_c({\mathbb R})$. We provide examples of relatively uniformly continuous semigroups such as Koopman semigroups and the Ornstein-Uhlenbeck semigroup. We introduce notions of relatively uniformly continuous, differentiable, and integrable functions on ${\mathbb R}_+$ which enable us to study generators of relatively uniformly continuous semigroups. Our main result is a Hille-Yosida type theorem which provides sufficient and necessary conditions for an operator to be the generator of an exponentially order bounded, relatively uniformly continuous, positive semigroup.20202020-09-25 08:15:22Doktorsko delo/naloga120744sl