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On the Ergodic Hilbert Transform for Operators In Lp, 1 < p < ∞

Published online by Cambridge University Press:  20 November 2018

Ryotaro Sato
Ryotaro Sato*
Affiliation:
Department of Mathematics School of Science Okayama University Okayama, 700 Japan
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Abstract

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In this paper the ergodic Hilbert transform is investigated at the operator theoretic level. Let T be an invertible positive operator on Lp = Lp(X, , μ) for some fixed p, 1 < p < ∞, such that sup{||Tn||p: — ∞ < n < ∞} < ∞. It is proved that the limit

exists almost everywhere and in the strong operator topology, where the prime denotes that the term with zero denominator is omitted. Related results are also proved.

Keywords

47A35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 210 - 214
Copyright
Copyright © Canadian Mathematical Society 1987

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