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Mean ergodic theorems on norming dual pairs

Published online by Cambridge University Press:  01 February 2013

MORITZ GERLACH  and
MARKUS KUNZE
MORITZ GERLACH
Affiliation:
University of Ulm, Institute of Applied Analysis, 89069 Ulm, Germany email [email protected]@uni-ulm.de
MARKUS KUNZE
Affiliation:
University of Ulm, Institute of Applied Analysis, 89069 Ulm, Germany email [email protected]@uni-ulm.de
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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 $({C}_{b} (E), \mathscr{M} (E))$ all classical equivalences hold true under an additional assumption which is slightly weaker than the e-property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1210 - 1229
Copyright
©2013 Cambridge University Press 

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