Let T be a power-bounded linear operator in a real Banach space X. We study the equality formula presented For X separable, we show that if T satisfies (*) and is not uniformly ergodic, then (I - T)X contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible Markov chains on the (positive) integers are obtained.
|Number of pages||19|
|State||Published - 1 Dec 1996|
ASJC Scopus subject areas
- Mathematics (all)