Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Ergodic theorems for semifinite von Neumann algebras: II

F. J. Yeadona1

a1 University of Hull

In (7) we proved maximal and pointwise ergodic theorems for transformations a of a von Neumann algebra S0305004100057418_xs1D4D0 which are linear positive and norm-reducing for both the operator norm xs2016 xs2016 and the integral norm xs2016 xs20161 associated with a normal trace ρ on S0305004100057418_xs1D4D0. 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

S0305004100057418_eqnU001

converge in norm.

(Received July 25 1979)