On mean ergodic theorems for positive operators in Lebesgue space

Ryotaro SATO

doi:10.2969/jmsj/02720207

Ryotaro SATO

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JOURNAL FREE ACCESS

1975 Volume 27 Issue 2 Pages 207-212

DOI https://doi.org/10.2969/jmsj/02720207

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Published: 1975 Received: March 05, 1973 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 and L. Sucheston, On operator convergence in Hilbert space and in Lebesgue space, Period. Math. Hungar., 2 (1972), 235-244.
2) R.V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
3) N. Dunford and J.T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
4) H. Fong, On invariant functions for positive operators, Colloq. Math., 22 (1970), 75-84.
5) U. Krengel and L. Sucheston, On mixing in infinite measure spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13 (1969), 150-164.
6) M. Lin, Mixing for Markov operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 19 (1971), 231-242.
7) M. Lin, Mixing of Cartesian squares of positive operators, Israel J. Math., 11 (1972), 349-354.
8) R. Sato, Ergodic properties of bounded L₁-operators, Proc. Amer. Math. Soc., 39 (1973), 540-546.
9) R. Sato, On Akcoglu and Sucheston's operator convergence theorem in Lebesgue space, Proc. Amer. Math. Soc., 40 (1973), 513-516.
10) L. Sucheston, On the ergodic theorem for positive operators I, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 8 (1967), 1-11.
11) L. Sucheston, Banach limits, Amer. Math. Monthly, 74 (1967), 308-311.

Right : [1] M. Akcoglu and L. Sucheston, On operator convergence in Hilbert space and in Lebesgue space, Period. Math. Hungar., 2 (1972), 235-244.
[2] R. V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc., 15 (1964), 553-559.
[3] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
[4] H. Fong, On invariant functions for positive operators, Colloq. Math., 22 (1970), 75-84.
[5] U. Krengel and L. Sucheston, On mixing in infinite measure spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13 (1969), 150-164.
[6] M. Lin, Mixing for Markov operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 19 (1971), 231-242.
[7] M. Lin, Mixing of Cartesian squares of positive operators, Israel J. Math., 11 (1972), 349-354.
[8] R. Sato, Ergodic properties of bounded L₁-operators, Proc. Amer. Math. Soc., 39 (1973), 540-546.
[9] R. Sato, On Akcoglu and Sucheston's operator convergence theorem in Lebesgue space, Proc. Amer. Math. Soc., 40 (1973), 513-516.
[10] L. Sucheston, On the ergodic theorem for positive operators I, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 8 (1967), 1-11.
[11] L. Sucheston, Banach limits, Amer. Math. Monthly, 74 (1967), 308-311.

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

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