Mean ergodic theorems for semigroups of positive linear operators

Fumio HIAI; Ryotaro SATO

doi:10.2969/jmsj/02910123

Fumio HIAI, Ryotaro SATO

著者情報

ジャーナルフリー

1977 年 29 巻 1 号 p. 123-134

DOI https://doi.org/10.2969/jmsj/02910123

詳細

Published: 1977 Received: 1976/02/05 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: 著者情報訂正内容: Wrong : Fumio HIAI¹⁾³⁾, Ryotaro SATO²⁾
Right : Fumio HIAI¹⁾²⁾, Ryotaro SATO³⁾

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) L. Alaoglu and G. Birkhoff, General ergodic theorems, Ann. of Math., 41 (1940), 293-309.
2) W.F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc., 67 (1949), 217-240.
3) M. M. Day, Amenable semigroups, Illinois J. Math., 1 (1957), 509-544.
4) M. M. Day, Fixed point theorems for compact convex sets, Illinois J. Math., 5 (1961), 585-590.
5) R.V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
6) N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
7) E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Pub., Vol. 31, Providence, R.I., 1957.
8) K. Jacobs, Neuere Methoden und Ergebnisse der Ergodentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960.
9) R. J. Nagel, Mittelergodische halbgruppen linearer operatoren, Ann. Inst. Fourier (Grenoble), 23-4 (1973), 75-87.
10) J. von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Nat. Acad. Sci. U.S.A., 18 (1932), 70-82.
11) W. Takahashi, Invariant functions for amenable semigroups of positive contractions on L¹, Kodai Math. Sem. Rep., 23 (1971), 131-143.
12) W. Takahashi, Ergodic theorems for amenable semigroups of positive contractions on L¹, Sci. Rep. Yokohama National Univ., 19 (1972), 5-11.

Right : [1] L. Alaoglu and G. Birkhoff, General ergodic theorems, Ann. of Math., 41 (1940), 293-309.
[2] W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc., 67 (1949), 217-240.
[3] M. M. Day, Amenable semigroups, Illinois J. Math., 1 (1957), 509-544.
[4] M. M. Day, Fixed point theorems for compact convex sets, Illinois J. Math., 5 (1961), 585-590.
[5] R. V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
[6] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
[7] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Pub., Vol. 31, Providence, R. I., 1957.
[8] K. Jacobs, Neuere Methoden und Ergebnisse der Ergodentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960.
[9] R. J. Nagel, Mittelergodische halbgruppen linearer operatoren, Ann. Inst. Fourier (Grenoble), 23-4 (1973), 75-87.
[10] J. von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Nat. Acad. Sci. U.S.A., 18 (1932), 70-82.
[11] W. Takahashi, Invariant functions for amenable semigroups of positive contractions on L¹, Kodai Math. Sem. Rep., 23 (1971), 131-143.
[12] W. Takahashi, Ergodic theorems for amenable semigroups of positive contractions on L¹, Sci. Rep. Yokohama National Univ., 19 (1972), 5-11.

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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