Ergodic properties of semi-Markovian operators on the Z1-part |
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| Authors: | A Ionescu Tulcea M Moretz |
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| Institution: | (1) Department of Mathematics, Northwestern University, 60201 Evanston, Illinois, USA;(2) Department of Mathematics, Kansas State University, Manhattan, Kansas, USA |
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| Abstract: | Summary In this note we consider a semi-Markovian operator, that is a positive linear mapping T: L
1  L
1 such that sup  T
n
< . We study the behavior of T
n
on the Z
1-part of the space (the  disappearing part in Sucheston's terminology). We show in particular, that if the operator T has a non-trivial conservative part in Z
1, then the ratio theorem must fail.Research supported by the U.S.Army Research Office (Durham) under contract DA-31-124-ARO(D)-288. |
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| Keywords: | |
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