Ergodic theorems for contraction semi-groups

Yoshihiro KUBOKAWA

doi:10.2969/jmsj/02720184

Yoshihiro KUBOKAWA

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JOURNAL FREE ACCESS

1975 Volume 27 Issue 2 Pages 184-193

DOI https://doi.org/10.2969/jmsj/02720184

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Published: 1975 Received: October 31, 1972 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Akcoglu, Pointwise ergodic theorems, Trans. Amer. Math. Soc., 125 (1966), 296-309.
2) M.A. Akcoglu and R.V. Chacon, A local ratio theorem, Canad. J. Math., 22 (1970), 545-552.
3) M. Akcoglu and J. Cunsolo, An ergodic theorem for semigroups, Proc. Amer. Math. Soc., 24 (1970), 166-170.
4) K. Berk, Ergodic theory with recurrent weights, Ann. Math. Statist., 39 (1968), 1107-1114.
5) R.V. Chacon, Convergence of operator averages, Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961), 89-120, Academic Press, New York, 1963.
6) R.V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
7) N. Dunford and J. Schwartz, Convergence almost everywhere of operator averages, J. Rat. Mech. Anal., 5 (1956), 129-178.
8) L.V. Kantrovic, Linear operators in semi-ordered spaces, I. Rec. Math. [Math. Sbornik) N.S., 49 (1940), 209-284.
9) U. Krengel, A local ergodic theorem, Invent. Math., 6 (1969), 329-333.
10) U. Krengel, Über den Absolutbetrag stetiger linearer Operatoren und seine Anwendungen auf ergodische Zerlegungen, Math. Scand., 13 (1963), 151-187.
11) Y. Kubokawa, A general local ergodic theorem, Proc. Japan Acad., 48 (1972), 461-465.
12) Y. Kubokawa, A local ergodic theorem for semi-group on L_p, Tohoku Math. J., 26 (1974), 411-422.
13) D. Ornstein, The sum of iterates of a positive operator, Advances in Probability and Related Topics (Edited by P. Ney), 2 (1970), 87-115.
14) T.R. Terrell, Local ergodic theorem for n-parameter semi-group of operators, Lecture Notes in Math., No. 160, 262-278, Springer, 1970.
15) T.R. Terrell, The local ergodic theorem and semi-groups of nonpositive operators, J. Functional Analysis, 10 (1972), 424-429.
16) S. Tsurumi, Ergodic theorems (Japanese), Sugaku, 13 (1961/62), 80-88.
17) S. Tsurumi, An ergodic theorem for a semigroup of linear contractions, Proc. Japan Acad., 49 (1973), 306-309.
18) K. Yosida, Functional Analysis, Springer, 1965.

Right : [1] M. Akcoglu, Pointwise ergodic theorems, Trans. Amer. Math. Soc., 125 (1966), 296-309.
[2] M. A. Akcoglu and R. V. Chacon, A local ratio theorem, Canad. J. Math., 22 (1970), 545-552.
[3] M. Akcoglu and J. Cunsolo, An ergodic theorem for semigroups, Proc. Amer. Math. Soc., 24 (1970), 166-170.
[4] K. Berk, Ergodic theory with recurrent weights, Ann. Math. Statist., 39 (1968), 1107-1114.
[5] R. V. Chacon, Convergence of operator averages, Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961), 89-120, Academic Press, New York, 1963.
[6] R. V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
[7] N. Dunford and J. Schwartz, Convergence almost everywhere of operator averages, J. Rat. Mech. Anal., 5 (1956), 129-178.
[8] L. V. Kantrovic, Linear operators in semi-ordered spaces, I. Rec. Math. [Math. Sbornik) N. S., 49 (1940), 209-284.
[9] U. Krengel, A local ergodic theorem, Invent. Math., 6 (1969), 329-333.
[10] U. Krengel, Über den Absolutbetrag stetiger linearer Operatoren und seine Anwendungen auf ergodische Zerlegungen, Math. Scand., 13 (1963), 151-187.
[11] Y. Kubokawa, A general local ergodic theorem, Proc. Japan Acad., 48 (1972), 461-465.
[12] Y. Kubokawa, A local ergodic theorem for semi-group on L_p, Tôhoku Math. J., 26 (1974), 411-422.
[13] D. Ornstein, The sum of iterates of a positive operator, Advances in Probability and Related Topics (Edited by P. Ney), 2 (1970), 87-115.
[14] T. R. Terrell, Local ergodic theorem for n-parameter semi-group of operators, Lecture Notes in Math., No. 160, 262-278, Springer, 1970.
[15] T. R. Terrell, The local ergodic theorem and semi-groups of nonpositive operators, J. Functional Analysis, 10 (1972), 424-429.
[16] S. Tsurumi, Ergodic theorems (Japanese), Sugaku, 13 (1961/62), 80-88.
[17] S. Tsurumi, An ergodic theorem for a semigroup of linear contractions, Proc. Japan Acad., 49 (1973), 306-309.
[18] K. Yosida, Functional Analysis, Springer, 1965.

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