1 results
Measurable and Continuous Units of an
$E_{0}$-semigroup
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 25 March 2020, pp. 469-478
- Print publication:
- June 2020
-
- Article
- Export citation
-
Let
$P$ be a closed convex cone in 
$\mathbb{R}^{d}$ which is spanning, i.e., 
$P-P=\mathbb{R}^{d}$ and pointed, i.e., 
$P\,\cap -P=\{0\}$. Let 
$\unicode[STIX]{x1D6FC}:=\{{\unicode[STIX]{x1D6FC}_{x}\}}_{x\in P}$ be an 
$E_{0}$-semigroup over 
$P$ and let 
$E$ be the product system associated to 
$\unicode[STIX]{x1D6FC}$. We show that there exists a bijective correspondence between the units of 
$\unicode[STIX]{x1D6FC}$ and the units of 
$E$.
