SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Compactifications, Hartman functions and (weak) almost periodicity

In this paper we investigate Hartman functions on a topological group G. Recall that (ι, C) is a group compactification of G if C is a compact group, ι : G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f : G 7→ C is a Hartman function if there exists a group compactification (ι, C) and F : C → C such that f = F ◦ ι and F is Riemann integrable, i.e. the set of ...

Topologically left invariant means on semigroup algebras

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

Periodicity and Almost-periodicity

Amenable Actions and Almost Invariant Sets

In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on MX , where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift Γ ↪→MX has almost invariant sets.

Almost Invariant Submanifolds for Compact Group Actions

A compact (not necessarily connected) Lie group G carries a (unique) biinvariant probability measure. Using this measure, one can average orbits of actions of G on affine convex sets to obtain fixed points. In particular, if G acts on a manifoldM , G leaves invariant a riemannian metric onM , and this metric can sometimes be used to obtain fixed points for the nonlinear action of G on M itself....