On the uniform ergodic theorem in Banach spaces that do not contain duals

Vladimir Fonf, Lin Michael, Alexander Rubinov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 languageEnglish
Pages (from-to)67-85
Number of pages19
JournalStudia Mathematica
Volume121
Issue number1
StatePublished - 1 Dec 1996

ASJC Scopus subject areas

  • General Mathematics

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