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Approximation of Lp-Contractions by Isometries

Part of: Markov processes

Published online by Cambridge University Press:  20 November 2018

M. A. Akcoglu  and
D. Boivin
M. A. Akcoglu
Affiliation:
Department of Mathematics University of Toronto Toronto, Ontario M5S 1A1 Canada
D. Boivin
Affiliation:
Department of Mathematics Ohio State University Columbus, Ohio 43210 U.S.A.
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Abstract

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We construct a positive linear contraction T of all LP(X, μ)- spaces, 1 ≦ p ≦ ∞, μ(X) = 1 such that T1 = 1, T* 1 = 1 and also Tf > 0 a.e. for all f ≧ 0 a.e., f ≢ 0 but for which there is an f ∊ L∞ such that (Tnf — ∫ fdμ) does not converge in L1-norm. We also show that if T is a contraction of a Hilbert space H, there exists an isometry Q and a contraction R such that ∥Tnx - QnRx∥ —> 0 as n —» ∞ for all x in H

MSC classification

Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 360 - 364
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Akcoglu, M. A. and L. Sucheston. An alternating procedure for operators in Lp-spaces. To appear.Google Scholar
2. Foguel, S. R.. Ergodic theory of Markov processes. Van Nostrand Math. Studies 21.Google Scholar
3. Kan, C. H.. On norming vectors and norm structures of linear operators between Lp spaces, I and II.To appear.Google Scholar
4. Revuz, D.. Markov Chains. North Holland Math. Library 11, North Holland American Elsevier (1975).Google Scholar
5. Rosenblatt, M.. Markov processes. Structure and asymptotic behavior. Springer, Berlin-Heidelberg, 1971.Google Scholar