## $L_ p$-continuity of positive semigroups on finite von Neumann algebras

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- by Seiji Watanabe
- Proc. Amer. Math. Soc.
**102**(1988), 840-842 - DOI: https://doi.org/10.1090/S0002-9939-1988-0934853-X
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## 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.## References

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## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- 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