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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Contractions on $ L\sb{1}$-spaces


Authors: M. A. Akcoglu and A. Brunel
Journal: Trans. Amer. Math. Soc. 155 (1971), 315-325
MSC: Primary 28.70; Secondary 47.00
DOI: https://doi.org/10.1090/S0002-9947-1971-0276439-0
MathSciNet review: 0276439
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Abstract: It is shown that a linear contraction on a complex $ {L_1}$-space can be represented in terms of its linear modulus. This result is then used to give a direct proof of Chacon's general ratio ergodic theorem.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0276439-0
Keywords: Contractions on $ {L_1}$-spaces, linear modulus of a contraction, ratio ergodic limits and their identification
Article copyright: © Copyright 1971 American Mathematical Society