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An elementary lemma on sequences of integers and its applications to functional analysis. (English) Zbl 0244.28010


MSC:

28D05 Measure-preserving transformations
47D99 Groups and semigroups of linear operators, their generalizations and applications
47A35 Ergodic theory of linear operators
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References:

[1] Akcoglu, M., Huneke, P., Rost, H.: A counterexample to the Blum-Hanson theorem in general spaces. As yet unpublished. · Zbl 0252.47006
[2] Blum, J.R., Hanson, D.L.: On the mean ergodic theorem for subsequences. Bull. Amer. Math. Soc.66, 308-311 (1960). · Zbl 0096.09005
[3] Friedman, N.A.: Introduction to ergodic theory. New York: Van Nostrand Reinhold 1970. · Zbl 0212.40004
[4] Friedman, N.A., Ornstein, D.S.: On partially mixing transformations. Ind. Univ. Math. Journal 20-8, 767-775 (1971). · Zbl 0213.07504
[5] Jacobs, K.: Ergodentheorie und fastperiodische Funktionen auf Halbgruppen. Math. Z.64, 298-338 (1956). · Zbl 0070.11701
[6] Jones, L.K.: Mixing operators. Unpublished, 1970.
[7] Jones, L.K.: A mean ergodic theorem for wearly mixing operators. To appear in Advances Math., December 1971.
[8] Jones, L.K., Kuftinek, V.: A note on the Blum-Hanson theorem. Proc. Amer. Math. Soc.30, 202-203 (1971). · Zbl 0218.28012
[9] Krengel, U.: Weakly wandering vectors and weakly independent partitions. To appear in Trans. Amer. Math. Soc. · Zbl 0205.13903
[10] Weyl, H.: Almost periodic invariant vector sets in a metric vector space. Amer. J. Math.71, 178-205 (1949). · Zbl 0032.03002
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