Two local ergodic theorems on L∞

Ryotaro SATO

doi:10.2969/jmsj/03230415

Two local ergodic theorems on L_∞

Ryotaro SATO

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 3 Pages 415-423

DOI https://doi.org/10.2969/jmsj/03230415

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Published: 1980 Received: April 28, 1978 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: SUBTITLE Details: Wrong : Dedicated to Professor Shisanji Hokari on his 70th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Ando, Contractive projections in L_p spaces, Pacific J. Math., 17 (1966), 391-405.
2) J. R. Baxter and R. V. Chacon, A local ergodic theorem on L_p, Canad. J. Math., 26 (1974), 1206-1216.
3) R. V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
4) R. G. Douglas, Contractive projections on an L₁ space, Pacific J. Math., 15 (1965), 443-462.
5) N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
6) C. Kipnis, Majoration des semi-groupes de contractions de L¹ et applications, Ann. Inst. H. Poincaré Sect. B (N. S.), 10 (1974), 369-384.
7) U. Krengel, A necessary and sufficient condition for the validity of the local ergodic theorem, Lecture Notes in Mathematics, No. 89, pp. 170-177, Springer, Berlin-Heidelberg-New York, 1969.
8) Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan, 27 (1975), 184-193.
9) M. Lin, Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), 20-44.
10) R. Sato, A note on a local ergodic theorem, Comment. Math. Univ. Carolinae, 16 (1975), 1-11.
11) R. Sato, On a local ergodic theorem, Studia Math., 58 (1976), 1-5.
12) R. Sato, Ergodic theorems for semigroups of positive operators, J. Math. Soc. Japan, 29 (1977), 591-606.
13) R. Sato, On local ergodic theorems for positive semigroups, Studia Math., 63 (1978), 45-55.
14) R. Sato, Contraction semigroups in Lebesgue space, Pacific J. Math., 78 (1978), 251-259.

Right : [1] T. Ando, Contractive projections in L_p spaces, Pacific J. Math., 17 (1966), 391-405.
[2] J. R. Baxter and R. V. Chacon, A local ergodic theorem on L_p, Canad. J. Math., 26 (1974), 1206-1216.
[3] R. V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
[4] R. G. Douglas, Contractive projections on an L₁ space, Pacific J. Math., 15 (1965), 443-462.
[5] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
[6] C. Kipnis, Majoration des semi-groupes de contractions de L¹ et applications, Ann. Inst. H. Poincaré Sect. B (N. S.), 10 (1974), 369-384.
[7] U. Krengel, A necessary and sufficient condition for the validity of the local ergodic theorem, Lecture Notes in Mathematics, No. 89, pp. 170-177, Springer, Berlin-Heidelberg-New York, 1969.
[8] Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan, 27 (1975), 184-193.
[9] M. Lin, Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), 20-44.
[10] R. Sato, A note on a local ergodic theorem, Comment. Math. Univ. Carolinae, 16 (1975), 1-11.
[11] R. Sato, On a local ergodic theorem, Studia Math., 58 (1976), 1-5.
[12] R. Sato, Ergodic theorems for semigroups of positive operators, J. Math. Soc. Japan, 29 (1977), 591-606.
[13] R. Sato, On local ergodic theorems for positive semigroups, Studia Math., 63 (1978), 45-55.
[14] R. Sato, Contraction semigroups in Lebesgue space, Pacific J. Math., 78 (1978), 251-259.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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