Linear semigroups with coarsely dense orbits

Details Linear semigroups with coarsely dense orbits Linear semigroups with coarsely dense orbits

2011-08-10

arxiv.org/abs/1108.2221v1

Mathematics

Functional Analysis

12 pages

Scientific paper

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional 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.

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