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Article

Hasegawa, Shigeru ; Sato, Ryotaro
On a $d$-parameter ergodic theorem for continuous semigroups of operators satisfying norm conditions. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 38 (1997), issue 3, pp. 453-462
MSC: 47A35, 47D06 | MR 1485067 | Zbl 0937.47009
Keywords:
vector valued multiparameter pointwise ergodic theorem; Chacon's ergodic theorem; semigroups of operators; norm conditions
Summary:
A continuous multiparameter version of Chacon's vector valued ergodic theorem is proved.
References:
[1] Brunel A., Émilion R.: Sur les opérateurs positifs à moyennes bornées. C.R. Acad. Sci. Paris Sér. I Math. 298 (1984), 103-106. MR 0741070
[2] Chacon R.V.: An ergodic theorem for operators satisfying norm conditions. J. Math. Mech. 11 (1962), 165-172. MR 0147619 | Zbl 0115.33804
[3] Dunford N., Schwartz J.T.: Linear Operators. Part I: General Theory. Interscience, New York, 1958. MR 1009162 | Zbl 0635.47001
[4] Hasegawa S., Sato R.: On $d$-parameter pointwise ergodic theorems in $L_1$. Proc. Amer. Math. Soc. 123 (1995), 3455-3465. MR 1249881
[5] Hasegawa S., Sato R., Tsurumi S.: Vector valued ergodic theorems for a one-parameter semigroup of linear operators. Tôhoku Math. J. 30 (1978), 95-106. MR 0467351 | Zbl 0377.47008
[6] Krengel U.: Ergodic Theorems. de Gruyter, Berlin, 1985. MR 0797411 | Zbl 0649.47042
[7] Sato R.: Vector valued differentiation theorems for multiparameter additive processes in $L_p$ spaces. submitted for publication. Zbl 0915.47012
[8] Terrell T.R.: Local ergodic theorems for $n$-parameter semigroups of operators. Lecture Notes in Math., vol. 160, Springer, Berlin, 1970, pp.262-278. MR 0268357 | Zbl 0204.45406
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