On the individual ergodic theorem for positive operators

Satō, Ryōtarō

doi:10.1090/S0002-9939-1972-0308820-1

On the individual ergodic theorem for positive operators
HTML articles powered by AMS MathViewer

by Ryōtarō Satō PDF

Proc. Amer. Math. Soc. 36 (1972), 456-458 Request permission

Abstract:

A theorem which gives a condition on a positive linear contraction on an ${L^1}$-space in order that the individual ergodic theorem hold is proved. The theorem contains a result obtained by Y. Ito as a special case.

References

M. A. Akcoglu and R. V. Chacon, A convexity theorem for positive operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1965), 328–332 (1965). MR 182710, DOI 10.1007/BF00535783
Glen Baxter, A general ergodic theorem with weighted averages, J. Math. Mech. 14 (1965), 277–288. MR 0174704
R. V. Chacon, Identification of the limit of operator averages, J. Math. Mech. 11 (1962), 961–968. MR 0145352
R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153–160. MR 110954
L. W. Cohen, On the mean ergodic theorem, Ann. of Math. (2) 41 (1940), 505–509. MR 2027, DOI 10.2307/1968732
Yuji Ito, Uniform integrability and the pointwise ergodic theorem, Proc. Amer. Math. Soc. 16 (1965), 222–227. MR 171895, DOI 10.1090/S0002-9939-1965-0171895-3
Ry\B{o}tar\B{o} Sat\B{o}, On a general ratio ergodic theorem with weighted averages, Proc. Amer. Math. Soc. 35 (1972), 177–178. MR 303317, DOI 10.1090/S0002-9939-1972-0303317-7