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Ergodic theorems for semifinite von Neumann algebras: II

Published online by Cambridge University Press:  24 October 2008

F. J. Yeadon
F. J. Yeadon
Affiliation:
University of Hull
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Extract

In (7) we proved maximal and pointwise ergodic theorems for transformations a of a von Neumann algebra which are linear positive and norm-reducing for both the operator norm ‖ ‖∞ and the integral norm ‖ ‖1 associated with a normal trace ρ on . Here we introduce a class of Banach spaces of unbounded operators, including the Lp spaces defined in (6), in which the transformations α reduce the norm, and in which the mean ergodic theorem holds; that is the averages

converge in norm.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 1 , July 1980 , pp. 135 - 147
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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