# On the ergodic theorem for positive operators

@inproceedings{Sucheston1967OnTE, title={On the ergodic theorem for positive operators}, author={Louis Sucheston}, year={1967} }

- Published 1967
DOI:10.1090/s0002-9904-1967-11769-5

Let (X, <$, /x) be a a-ûnite measure space and let T be a positive linear operator on Li(X, Cfc, ix). The ratio ergodic theorem of ChaconOrnstein (see [3], [7], [2]) assumes that | JT|I, the Li norm of T, is less than or equal to one. Here we discuss the behavior of the ratio under the weaker boundedness assumption (fa). All sets and functions introduced below are assumed measurable. All relations are assumed to hold modulo sets of /x-measure zero. L* is the class of nonnegative not identically… CONTINUE READING

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