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On one-parameter Koopman groups

Published online by Cambridge University Press:  28 December 2015

A. F. M. ter ELST  and
M. LEMAŃCZYK
A. F. M. ter ELST
Affiliation:
Department of Mathematics, University of Auckland, Private bag 92019, Auckland 1142, New Zealand email terelst@math.auckland.ac.nz
M. LEMAŃCZYK
Affiliation:
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 12/18 Chopin street, 87-100 Toruń, Poland email mlem@mat.umk.pl
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Abstract

We characterize Koopman one-parameter $C_{0}$-groups, in the class of all unitary one-parameter $C_{0}$-groups on $L_{2}(X)$, as those that preserve $L_{\infty }(X)$ and for which the infinitesimal generator is a derivation on the bounded functions in its domain.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 5 , August 2017 , pp. 1635 - 1656
Copyright
© Cambridge University Press, 2015 

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