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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive contractions on $L_{1}$-spaces
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by Ryōtarō Satō PDF
Proc. Amer. Math. Soc. 42 (1974), 442-444 Request permission

Abstract:

Let T be a positive linear operator on ${L_1}$ of a probability space such that ${\left \| T \right \|_1} \leqq 1$. In this note we consider the following question: Under what condition is T multiplicative on ${L_\infty }$?
References
  • Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
  • Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, vol. 3, Mathematical Society of Japan, Tokyo, 1956. MR 0097489
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 442-444
  • MSC: Primary 47A35
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0390806-4
  • MathSciNet review: 0390806