In this note we use the term graph for simple, connected, undirected graphs with bounded degree vertices only. We will mostly consider infinite graphs. We denote the set of vertices of a graph G by V (G), we use E(G) for the set of edges. By ~ E(G) we denote the set of oriented edges: ~ E(G) = {(x, y) | {x, y} ∈ E(G)}. We denote the opposite orientation (y, x) of an oriented edge e = (x, y) by ...

In 1931, Birkhoff gave a general and rigorous description of the ergodic hypothesis from statistical meachanics. This concept can be generalized by group actions of a large class of amenable groups on σ-finite measure spaces. The expansion of this theory culminated in Lindenstrauss’ celebrated proof of the general pointwise ergodic theorem in 2001. The talk is devoted to the introduction of abs...

We give an example of an amenable, radical Banach algebra, relying on results from non-abelian harmonic analysis due to H. Leptin, D. Poguntke and J. Boidol. Let A be a Banach algebra, and let E be a Banach A-module. A bounded linear map D : A → E is called a a derivation if D(ab) = a.Db+ (Da).b (a, b ∈ A). A derivation D : A → E is said to be inner if Da = x.a− a.x (a ∈ A) for some x ∈ E. For ...