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Semi-Groups in L∞ And Local Ergodic Theorem

Published online by Cambridge University Press:  20 November 2018

R. Emilion
R. Emilion*
Affiliation:
Université Paris Vi Laboratoire de Probabilités 4, Place Jussieu 75230, Paris Cedex 05
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Abstract

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We show that any W*-continuous semi-group in L∞ is L1-norm continuous. As an application we prove the n-dimensional local ergodic theorem in L∞. We also note that any bounded additive process in L∞ is absolutely continuous.

For n = 1 this local theorem improves those of R. Sato [14] and D. Feyel [6] and for n ≥ 1 it generalizes M. Lin's ones which hold for positive operators [12].

Keywords

47A3547D0528A65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 146 - 153
Copyright
Copyright © Canadian Mathematical Society 1986

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