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An Abstract Version of a Result of Fong and Sucheston

Published online by Cambridge University Press:  20 November 2018

P. E. Kopp
P. E. Kopp*
Affiliation:
Department of Pure Mathematics, University of Hull, England
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Nagel [3] has given a purely functional-analytic proof of Akcoglu and Sucheston's operator version [1] of the Blum-Hanson theorem. The purpose of this note is to show that the same techniques may be applied to obtain a proof, in the context of (AL)-spaces, of a more general result due to Fong and Sucheston [2]. By Kakutani's representation theorem, any (AL)-space can of course be represented as an L-1-space. Thus the present result is simply a reformulation of that of Fong and Sucheston.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 2 , 01 June 1978 , pp. 247 - 248
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Akcoglu, M. A. and Sucheston, L.: On operator convergence in Hilbert space and in Lebesgue space. Per. Math. Hung. 2 (1972), 235-244.Google Scholar
2. Fong, H. and Sucheston, L.. On a mixing property of operators in Lp spaces. Z. Wahrscheinlichkeitstheorie u. verw. Gebiete 28 (1974), 165-171.Google Scholar
3. Nagel, R. J.. Ergodic and mixing properties of linear operators. Proc. R.I.A., Vol. 74, Sect. A, (1974), 245-261.Google Scholar
4. Schaefer, H. H.: Banach lattices and positive operators. Springer, 1975.Google Scholar