Measurable and Continuous Units of an E0-semigroup

Abstract

Let 𝑃 be a closed convex cone in ℝ𝑑 which is spanning, i.e., 𝑃−𝑃=ℝ𝑑 and pointed, i.e., 𝑃∩−𝑃={0} . Let 𝛼:={𝛼𝑥}𝑥∈𝑃 be an 𝐸0 -semigroup over 𝑃 and let 𝐸 be the product system associated to 𝛼 . We show that there exists a bijective correspondence between the units of 𝛼 and the units of 𝐸 .