Addits in time ordered product systems

Abstract

In this paper we observe the set of all continuous additive units (continuous addits) of the vacuum unit ω in the time ordered product system IΓ⊗(F), where F is a two-sided Hilbert module over the C∗-algebra B of all bounded operators acting on a Hilbert space of finite dimension. We prove that the set of all continuous addits of ω and F⊕B are isomorphic as Hilbert B-B modules.