Inner amenable semigroups I

Subsemigroups of Cancellative Amenable Semigroups

We generalize a theorem of Frey by giving sufficient conditions for a subsemigroup T of a cancellative left amenable semigroup S to be left amenable. In particular, we show that if S is left amenable and T does not contain a free subsemigroup on two generators, then T is left amenable as well.

A CHARACTERIZATION OF EXTREMELY AMENABLE SEMIGROUPS

Let S be a discrete semigroup, m (S) the space of all bounded real functions on S with the usualsupremum norm. Let Acm (S) be a uniformly closed left invariant subalgebra of m (S) with 1 c A. We say that A is extremely left amenable if there isamultiplicative left invariant meanon A. Let P = {h ?A: h =|g-1,g | forsome g ?A, s ?S}. It isshown that . A is extremely left amenable if and only ...

Structural Properties of Inner Amenable Discrete Groups

structural properties of inner amenable discrete groups

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup (S, ·) as follows: Players 1 and 2 choose elements x ∈ S and y ∈ S, respectively, and player 1 receives a payoff f(xy) defined by a function f : S → [−1, 1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, ...