# On a $d$-parameter ergodic theorem for continuous semigroups of operators satisfying norm conditions

Shigeru Hasegawa; Ryotaro Sato

Commentationes Mathematicae Universitatis Carolinae (1997)

- Volume: 38, Issue: 3, page 453-462
- ISSN: 0010-2628

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topHasegawa, Shigeru, and Sato, Ryotaro. "On a $d$-parameter ergodic theorem for continuous semigroups of operators satisfying norm conditions." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 453-462. <http://eudml.org/doc/248044>.

@article{Hasegawa1997,

abstract = {A continuous multiparameter version of Chacon's vector valued ergodic theorem is proved.},

author = {Hasegawa, Shigeru, Sato, Ryotaro},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {vector valued multiparameter pointwise ergodic theorem; Chacon's ergodic theorem; semigroups of operators; norm conditions; semigroups of operators; pointwise ergodic theorem},

language = {eng},

number = {3},

pages = {453-462},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On a $d$-parameter ergodic theorem for continuous semigroups of operators satisfying norm conditions},

url = {http://eudml.org/doc/248044},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Hasegawa, Shigeru

AU - Sato, Ryotaro

TI - On a $d$-parameter ergodic theorem for continuous semigroups of operators satisfying norm conditions

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1997

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 38

IS - 3

SP - 453

EP - 462

AB - A continuous multiparameter version of Chacon's vector valued ergodic theorem is proved.

LA - eng

KW - vector valued multiparameter pointwise ergodic theorem; Chacon's ergodic theorem; semigroups of operators; norm conditions; semigroups of operators; pointwise ergodic theorem

UR - http://eudml.org/doc/248044

ER -

## References

top- Brunel A., Émilion R., Sur les opérateurs positifs à moyennes bornées, C.R. Acad. Sci. Paris Sér. I Math. 298 (1984), 103-106. (1984) MR0741070
- Chacon R.V., An ergodic theorem for operators satisfying norm conditions, J. Math. Mech. 11 (1962), 165-172. (1962) Zbl0115.33804MR0147619
- Dunford N., Schwartz J.T., Linear Operators. Part I: General Theory, Interscience, New York, 1958. Zbl0635.47001MR1009162
- Hasegawa S., Sato R., On $d$-parameter pointwise ergodic theorems in ${L}_{1}$, Proc. Amer. Math. Soc. 123 (1995), 3455-3465. (1995) MR1249881
- 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. (1978) Zbl0377.47008MR0467351
- Krengel U., Ergodic Theorems, de Gruyter, Berlin, 1985. Zbl0649.47042MR0797411
- Sato R., Vector valued differentiation theorems for multiparameter additive processes in ${L}_{p}$ spaces, submitted for publication. Zbl0915.47012
- Terrell T.R., Local ergodic theorems for $n$-parameter semigroups of operators, Lecture Notes in Math., vol. 160, Springer, Berlin, 1970, pp.262-278. Zbl0204.45406MR0268357

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