Positive contractions on $L_{1}$-spaces
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- by Ryōtarō Satō
- Proc. Amer. Math. Soc. 42 (1974), 442-444
- DOI: https://doi.org/10.1090/S0002-9939-1974-0390806-4
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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
Bibliographic 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