An analogue of Fekete's lemma for subadditive functions on cancellative amenable semigroups

TL;DR

This paper extends Fekete's lemma to subadditive, right-subinvariant functions on finite subsets of cancellative left-amenable semigroups, broadening its applicability beyond groups.

Contribution

It introduces an analogue of Fekete's lemma for a new class of algebraic structures, namely cancellative left-amenable semigroups, generalizing previous group-based results.

Findings

Established Fekete's lemma analogue for semigroups

Extended previous group results to semigroups

Broadened the scope of subadditive function analysis

Abstract

We prove an analogue of Fekete's lemma for subadditive right-subinvariant functions defined on the finite subsets of a cancellative left-amenable semigroup. This extends results previously obtained in the case of amenable groups by E. Lindenstrauss and B. Weiss and by M. Gromov.