1 results
MEASURABLE
$E_{0}$-SEMIGROUPS ARE CONTINUOUS
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society / Volume 111 / Issue 2 / October 2021
- Published online by Cambridge University Press:
- 04 December 2019, pp. 278-288
- Print publication:
- October 2021
-
- Article
- Export citation
-
Let
$G$ be a second countable locally compact Hausdorff topological group and 
$P$ be a closed subsemigroup of 
$G$ containing the identity element 
$e\in G$. Assume that the interior of 
$P$ is dense in 
$P$. Let 
$\unicode[STIX]{x1D6FC}=\{{\unicode[STIX]{x1D6FC}_{x}\}}_{x\in P}$ be a semigroup of unital normal 
$\ast$-endomorphisms of a von Neumann algebra 
$M$ with separable predual satisfying a natural measurability hypothesis. We show that 
$\unicode[STIX]{x1D6FC}$ is an 
$E_{0}$-semigroup over 
$P$ on 
$M$.
