Mean ergodic theorems on norming dual pairs (Q2925263)

In the present paper, the classical mean ergodic theorem is extended to the setting of norming dual pairs. In Section~2, the authors give basic definitions and discuss results about norming dual pairs \((X,Y, \langle \cdot, \cdot \rangle)\), where \(X,Y\) are Banach spaces and \(\langle \cdot, \cdot \rangle\) is a duality between \(X\) and \(Y\). In Section~3, they introduce the notion of an ``average scheme'', which are further analyzed in Section~4. In Section 5, the authors consider the convergence of average schemes on \((C_b (E), \mathcal{M} (E))\) under additional assumptions. In Section~6, they provide some counterexamples.