Geodesic
An Abstract Version of a Result of Fong and Sucheston
Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 247-248

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Kopp, P. E. An Abstract Version of a Result of Fong and Sucheston. Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 247-248. doi: 10.4153/CMB-1978-042-5
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[1] 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] 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] 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] 4. Schaefer, H. H.: Banach lattices and positive operators. Springer, 1975. Google Scholar

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