%0 Journal Article
%T Linear semigroups with coarsely dense orbits
%A Herbert Abels
%A Antonios Manoussos
%J Mathematics
%D 2011
%I arXiv
%X Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit contains a coarsely dense subset of some open cone $C$ in $V$ then the closure of the orbit contains the closure of $C$. In the complex case the orbit is then actually dense in $V$. For the real case we give precise information about the possible cases for the closure of the orbit.
%U http://arxiv.org/abs/1108.2221v2