Mean ergodic theorems on norming dual pairs

TL;DR

This paper extends the classical mean ergodic theorem to norming dual pairs, showing that classical equivalences hold for Markovian semigroups under a mild additional assumption.

Contribution

It generalizes the mean ergodic theorem to norming dual pairs and identifies conditions under which classical equivalences are valid.

Findings

Classical equivalences hold for Markovian semigroups on (C_b(E), M(E))

Not all equivalences from Banach space setting remain valid in norming dual pairs

A weaker-than-e-property condition ensures classical results

Abstract

We extend the classical mean ergodic theorem to the setting of norming dual pairs. It turns out that, in general, not all equivalences from the Banach space setting remain valid in our situation. However, for Markovian semigroups on the norming dual pair (C_b(E), M(E)) all classical equivalences hold true under an additional assumption which is slightly weaker than the e-property.