Rokhlin-Type Properties of Group Actions on Operator Algebras

There are two major classes of objects in the theory of operator algebras, namely C∗-algebras and von Neumann algebras. These are subalgebras of the set of bounded operators B(H) on a complex Hilbert space H, which are respectively closed in norm and weak operator topology. By the celebrated Gelfand-Naimark theorem, any abelian C∗-algebra is isomorphic to the algebra C0(X) of continuous functions vanishing at infinity on a locally compact Hausdorff space X, thereby, C∗-algebras are sometimes regarded as noncommutative analogues of topological spaces, while von Neumann algebras are regarded as analogues of measure spaces.