SAMS Subject Classification Number: 11

In this talk, we will introduce the notion of a positive weighted (Koopman) semigroup representation on a Banach lattice-module over the (Koopman) group representation on a commutative Banach lattice-algebra. For topological dynamics, we obtain the abstract representation of the space of continuous sections vanishing at “infinity” of a topological Banach lattice-bundle (over a locally compact space \(\Omega\)) as an AM m-lattice-module over \(C_0(\Omega)\) on which every positive weighted semigroup is isomorphic to the positive weighted Koopman group representation induced by the unique dynamics on the underlying topological Banach lattice-bundle.