Inner invariant means on discrete semigroups with identity

INNER INVARIANT MEANS ON DISCRETE SEMIGROUPS WITH IDENTITY

B. Mohammadzadeh 

R. Nasr-Isfahani

Abstract: In the present paper, we initiate a study of a concept of amenability for
discrete semigroups S with identity called strict inner amenability. We first study
the relations between the concepts inner amenability, strict inner amenability, and
amenability of S. We then introduce some suitable tools and properties to give several
characterizations of strict inner amenability of S such as Reiter’s condition and Følner’s
condition. We also offer a characterization of strict inner amenability in terms of a
fixed point property. As applications of these results to discrete groups G, we obtain
a number of equivalent statements describing strict inner amenability of G.