| Title:
|
On a $d$-parameter ergodic theorem for continuous semigroups of operators satisfying norm conditions (English) |
| Author:
|
Hasegawa, Shigeru |
| Author:
|
Sato, Ryotaro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
453-462 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A continuous multiparameter version of Chacon's vector valued ergodic theorem is proved. (English) |
| Keyword:
|
vector valued multiparameter pointwise ergodic theorem |
| Keyword:
|
Chacon's ergodic theorem |
| Keyword:
|
semigroups of operators |
| Keyword:
|
norm conditions |
| MSC:
|
47A35 |
| MSC:
|
47D06 |
| idZBL:
|
Zbl 0937.47009 |
| idMR:
|
MR1485067 |
| . |
| Date available:
|
2009-01-08T18:35:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118944 |
| . |
| Reference:
|
[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 |
| Reference:
|
[2] Chacon R.V.: An ergodic theorem for operators satisfying norm conditions.J. Math. Mech. 11 (1962), 165-172. Zbl 0115.33804, MR 0147619 |
| Reference:
|
[3] Dunford N., Schwartz J.T.: Linear Operators. Part I: General Theory.Interscience, New York, 1958. Zbl 0635.47001, MR 1009162 |
| Reference:
|
[4] Hasegawa S., Sato R.: On $d$-parameter pointwise ergodic theorems in $L_1$.Proc. Amer. Math. Soc. 123 (1995), 3455-3465. MR 1249881 |
| Reference:
|
[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. Zbl 0377.47008, MR 0467351 |
| Reference:
|
[6] Krengel U.: Ergodic Theorems.de Gruyter, Berlin, 1985. Zbl 0649.47042, MR 0797411 |
| Reference:
|
[7] Sato R.: Vector valued differentiation theorems for multiparameter additive processes in $L_p$ spaces.submitted for publication. Zbl 0915.47012 |
| Reference:
|
[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. Zbl 0204.45406, MR 0268357 |
| . |
