On the Ergodic Theorem without Assumption of Positivity by R. v. Chacon

@inproceedings{Oxtoby2007OnTE,
  title={On the Ergodic Theorem without Assumption of Positivity by R. v. Chacon},
  author={John C. Oxtoby},
  year={2007}
}
  • John C. Oxtoby
  • Published 2007
0. Introduction, Dunford and Schwartz [3; 5] have recently obtained a generalization of an ergodic theorem of E. Hopf [4] to include nonpositive operators in spaces of complex valued functions. Their method of proof is to majorize the operator in question by a positive one, and then to apply Hopf's results. We give a direct proof of a maximal ergodic lemma for operators which are not necessarily positive, in spaces of functions which take their values in an arbitrary Banach space. This lemma is… CONTINUE READING

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

Abstract Ergodic Theoremso)

ALEXANDRA IONESCU TULCEA, CASSIUS IONESCU TULCEA
2010
View 4 Excerpts
Highly Influenced

References

Publications referenced by this paper.
Showing 1-5 of 5 references

A general ergodic theorem

R. V. Chacon, D. S. Ornstein
Illinois J. Math, vol • 1960

Another proof of E. Hopf s ergodic lemma, Comm

J. T. Schwartz
Pure Appl. Math. vol • 1959

A vector valued random ergodic theorem

A. Beck, J. T. Schwartz
Proc. Airier. Math. Soc. vol • 1957

Convergence Almost Everywhere of Operator Averages.

Proceedings of the National Academy of Sciences of the United States of America • 1955

The general temporally discrete Markoff process

E. Hopf
J. Math. Mech. vol • 1954
View 1 Excerpt

Similar Papers

Loading similar papers…