Article contents
The return times and the Wiener—Wintner property for mean-bounded positive operators in Lp
Published online by Cambridge University Press: 19 September 2008
Abstract
We prove the following two results for mean-bounded positive operators on Lp(µ) (1<p>∞).
(1) If (X, , µ, ϕ) is a dynamical system and f ∈ L∞ (X) then the sequence f(ϕn x) is a.e. a universal good sequence for mean-bounded positive operators in Lp. (Return times property.)
(2) If T is a mean-bounded positive operator on LP(X, , µ) and f ∈ Lp (µ) then the sequence Tnf)(x) is a.e. a universal good sequence for all dynamical systems (Y, , v,S) in L∞(v). A corollary of (2) is a Wiener-Wintner property for mean-bounded positive operators on Lp.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 1992
References
REFERENCES
- 2
- Cited by