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  $E$ .

让 $ P $ 是在一个封闭的凸锥 $ \ mathbb {R} ^ {d} $ 这是跨越，即， $ PP = \ mathbb {R} ^ {d} $ 和尖，即， $ P \，\ cap -P = \ {0 \} $ 。假设 $ \ unicode [STIX] {x1D6FC}：= \ {{\ unicode [STIX] {x1D6FC} _ {x} \}} _ {x \ in P} $ 为 $ E_ {0} $ -超过 $的半组 P $ 并令 $ E $ 为与 $ \ unicode [STIX] {x1D6FC} $ 相关的产品系统。我们证明 $ \ unicode [STIX] {x1D6FC} $ 的单位和 $ E $ 的单位 之间存在双射对应 。