Arveson's characterisation of CCR flows: The multiparameter case

摘要

In this paper, we revisit Arveson's characterisation of CCR flows in terms of the decomposability of the product system in the multiparameter context. We show that a multiparameter E-0-semigroup is a CCR flow if and only if it is decomposable and admits a unit. In contrast to the one parameter situation, we exhibit uncountably many examples of decomposable E-0-semigroups which do not admit any unit. As applications, we show that for a pure isometric representation V, the associated CCR flow alpha(V) remembers the unitary equivalence class of V, compute the positive contractive as well as the projective local cocycles of a CCR flow and derive a necessary and a sufficient condition for a CCR flow to be prime. (C) 2020 Elsevier Inc. All rights reserved.