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On dynamical systems preserving weights

Published online by Cambridge University Press:  03 April 2017

LAVY KOILPITCHAI  and
KUNAL MUKHERJEE
LAVY KOILPITCHAI
Affiliation:
Indian Institute of Technology Madras, Chennai 600 036, India email [email protected], [email protected]
KUNAL MUKHERJEE
Affiliation:
Indian Institute of Technology Madras, Chennai 600 036, India email [email protected], [email protected]
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Abstract

The canonical unitary representation of a locally compact separable group arising from an ergodic action of the group on a von Neumann algebra with separable predual preserving a faithful normal semifinite (infinite) weight is weak mixing. On the contrary, there exists a non-ergodic automorphism of a von Neumann algebra preserving a faithful normal semifinite trace such that the spectral measure and the spectral multiplicity of the induced action are respectively the Haar measure (on the unit circle) and $\infty$. Despite not even being ergodic, this automorphism has the same spectral data as that of a Bernoulli shift.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 7 , October 2018 , pp. 2729 - 2747
Copyright
© Cambridge University Press, 2017 

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