Arveson's characterisation of CCR flows: The multiparameter case

In this paper, we revisit Arveson's characterisation of CCR flows in terms the decomposability product system multiparameter context. We show that a E0-semigroup is flow if and only it decomposable admits unit. contrast to one parameter situation, exhibit uncountably many examples E0-semigroups which do not admit any As applications, for pure isometric representation V, associated αV remembers unitary equivalence class compute positive contractive as well projective local cocycles derive necessary sufficient condition be prime.