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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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 }$?

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Additional Information

PII: S 0002-9939(1974)0390806-4
Keywords: Positive contraction, multiplicative, measure algebra, homomorphism of a measure algebra
Article copyright: © Copyright 1974 American Mathematical Society