Ergodic theorems for semigroups of positive operators

Ryotaro SATO

doi:10.2969/jmsj/02940591

Ryotaro SATO

著者情報

ジャーナルフリー

1977 年 29 巻 4 号 p. 591-606

DOI https://doi.org/10.2969/jmsj/02940591

詳細

Published: 1977 Received: 1974/02/18 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M.A. Akcoglu and J. Cunsolo, An ergodic theorem for semigroups, Proc. Amer. Math. Soc., 24 (1970), 161-170.
2) K.N. Berk, Ergodic theory with recurrent weights, Ann. of Math. Statist., 39 (1968), 1107-1114.
3) R.V. Chacon and D.S. Ornstein, A general ergodic theorem, Illinois J. Math., 4 (1960), 153-160.
4) Y. Derriennic and M. Lin, On invariant measures and ergodic theorems for positive operators, J. Functional Analysis, 13 (1973), 252-267.
5) N. Dunford and J. T. Schwartz, Convergence almost everywhere of operator averages, J. Rational Mech. Anal., 5 (1956), 129-178.
6) N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience Publishers, New York, 1958.
7) H. Fong and L. Sucheston, On the ratio ergodic theorem for semi-groups, Pacific J. Math., 39 (1971), 659-667.
8) H. Fong and L. Sucheston, On unaveraged convergence of positive operators in Lebesgue space, Trans. Amer. Math. Soc., 179 (1973), 383-397.
9) S. Hasegawa and R. Sato, A general ratio ergodic theorem for semigroups, Pacific J. Math., 62 (1976), 435-437.
10) G. Helmberg, On the converse of Hopf's ergodic theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 21 (1972), 77-80.
11) Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan, 27 (1975), 184-193.
12) M. Lin, Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), 20-44.
13) R. Sato, On the individual ergodic theorem for positive operators, Proc. Amer. Math. Soc., 36 (1972), 456-458.
14) R. Sato, Ergodic properties of bounded L₁-operators, Proc. Amer. Math. Soc., 39 (1973), 540-546.
15) R. Sato, Invariant measures for semigroups, Studia Math., 53 (1975), 129-134.
16) R. Sato, A mean ergodic theorem, Amer. Math. Monthly, 82 (1975), 487-488.
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-Verlag, Berlin-Göttingen-Heidelberg, 1965.
19) K. Yosida and S. Kakutani, Operator-theoretical treatment of Markoff's process and mean ergodic theorem, Ann. of Math., (2) 42 (1941), 188-228.

Right : [1] M. A. Akcoglu and J. Cunsolo, An ergodic theorem for semigroups, Proc. Amer. Math. Soc., 24 (1970), 161-170.
[2] K. N. Berk, Ergodic theory with recurrent weights, Ann. of Math. Statist., 39 (1968), 1107-1114.
[3] R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math., 4 (1960), 153-160.
[4] Y. Derriennic and M. Lin, On invariant measures and ergodic theorems for positive operators, J. Functional Analysis, 13 (1973), 252-267.
[5] N. Dunford and J. T. Schwartz, Convergence almost everywhere of operator averages, J. Rational Mech. Anal., 5 (1956), 129-178.
[6] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience Publishers, New York, 1958.
[7] H. Fong and L. Sucheston, On the ratio ergodic theorem for semi-groups, Pacific J. Math., 39 (1971), 659-667.
[8] H. Fong and L. Sucheston, On unaveraged convergence of positive operators in Lebesgue space, Trans. Amer. Math. Soc., 179 (1973), 383-397.
[9] S. Hasegawa and R. Sato, A general ratio ergodic theorem for semigroups, Pacific J. Math., 62 (1976), 435-437.
[10] G. Helmberg, On the converse of Hopf's ergodic theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 21 (1972), 77-80.
[11] Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan, 27 (1975), 184-193.
[12] M. Lin, Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), 20-44.
[13] R. Sato, On the individual ergodic theorem for positive operators, Proc. Amer. Math. Soc., 36 (1972), 456-458.
[14] R. Sato, Ergodic properties of bounded L₁-operators, Proc. Amer. Math. Soc., 39 (1973), 540-546.
[15] R. Sato, Invariant measures for semigroups, Studia Math., 53 (1975), 129-134.
[16] R. Sato, A mean ergodic theorem, Amer. Math. Monthly, 82 (1975), 487-488.
[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-Verlag, Berlin-Göttingen-Heidelberg, 1965.
[19] K. Yosida and S. Kakutani, Operator-theoretical treatment of Markoff's process and mean ergodic theorem, Ann. of Math., (2) 42 (1941), 188-228.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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