Abstract
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.
Original language | English |
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Pages (from-to) | 67-85 |
Number of pages | 19 |
Journal | Studia Mathematica |
Volume | 121 |
Issue number | 1 |
State | Published - 1 Dec 1996 |
ASJC Scopus subject areas
- General Mathematics