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Probabilistic Proofs of the Little Riesz Theorem

Published online by Cambridge University Press:  20 November 2018

A. N. Al-Hussaini
A. N. Al-Hussaini*
Affiliation:
Department of Math. University of Alberta, Edmonton, Alberta T6G 2G1
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The following theorem is a widely used corollary of the Thorn-Riesz convexity theorem ([1], pp. 526).

Theorem. Let (Ω, a, μ) be a positive measure space, and let

be a linear operator with ‖T‖1≤1, ‖T‖∞≤1. Then ‖T‖p≤1, 1≤p≤∞

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 443 - 445
Copyright
Copyright © Canadian Mathematical Society 1977

References

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3. Lacey, H.E., The isometric theory of classical Banach spaces, Berlin, Springer-Verlag, 1974.Google Scholar
4. Rosenblatt, M., Markov processes; structure and asymptotic behavior, Berlin, Springer-Verlag, 1971.Google Scholar
5. Schaefer, H.H., Banach Lattices and Positive Operators. Springer-Verlag, 1974.Google Scholar