ON THE ERGODIC HILBERT TRANSFORM IN
OVER A VON NEUMANN ALGEBRA
Abstract: In this note a noncommutative version of Jajte’s theorem on the existence of the ergodic
Hubert transform is given. As a noncommutative counterpart of the classical almost everywhere
convergence the bundle convergence of operators in a von Neumann algebra and its
-space
is used.
2000 AMS Mathematics Subject Classification: Primary: 46L53, 60F15, 47A35;
Secondary: 42C15.
Key words and phrases: Ergodic Hubert transform, von Neumann algebra, bundle
convergence.