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Proceedings of the American Mathematical Society

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Positive contractions on $ L\sb{1}$-spaces

Author: Ryōtarō Satō
Journal: Proc. Amer. Math. Soc. 42 (1974), 442-444
MSC: Primary 47A35
MathSciNet review: 0390806
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Abstract: Let T be a positive linear operator on $ {L_1}$ of a probability space such that $ {\left\Vert T \right\Vert _1} \leqq 1$. In this note we consider the following question: Under what condition is T multiplicative on $ {L_\infty }$?

References [Enhancements On Off] (What's this?)

  • [1] L. Gillman and M. Jerison, Rings of continuous functions, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #6994. MR 0116199 (22:6994)
  • [2] P. R. Halmos, Lectures on ergodic theory, Publ. Math. Soc. Japan, no. 3, Math. Soc. of Japan, Tokyo, 1956. MR 20 #3958. MR 0097489 (20:3958)

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Keywords: Positive contraction, multiplicative, measure algebra, homomorphism of a measure algebra
Article copyright: © Copyright 1974 American Mathematical Society

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