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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

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