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

  title={On the Ergodic Theorem without Assumption of Positivity by R. v. Chacon},
  author={John C. Oxtoby},
  • 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

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