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Contents of PMS, Vol. 27, Fasc. 2,
pages 223 - 234
 

ON THE ERGODIC HILBERT TRANSFORM IN $L_2$ OVER A VON NEUMANN ALGEBRA

Katarzyna Kielanowicz

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 $L_2$-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.

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