Article contents
Measurable and Continuous Units of an
$E_{0}$-semigroup
Published online by Cambridge University Press: 25 March 2020
Abstract
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
$E$.
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- © Canadian Mathematical Society 2019
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