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$ L\sb p$-continuity of positive semigroups on finite von Neumann algebras


Author: Seiji Watanabe
Journal: Proc. Amer. Math. Soc. 102 (1988), 840-842
MSC: Primary 46L10; Secondary 46L40, 47D05
DOI: https://doi.org/10.1090/S0002-9939-1988-0934853-X
MathSciNet review: 934853
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a $ \sigma $-finite, finite von Neumann algebra with a faithful normal tracial state $ \tau $. Let $ \alpha $ be a one-parameter semigroup of normal positive contractions of $ M$. Then it is shown that $ \alpha $ is continuous with respect to the $ {L_p}$-norm $ (1 \leq p < \infty )$ induced by $ \tau $ if and only if it is $ \sigma $-weakly continuous.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934853-X
Keywords: Positive semigroup, trace, finite von Neumann algebra
Article copyright: © Copyright 1988 American Mathematical Society

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