On the index and roots of time ordered product systems

Abstract

In this paper, motivated by Bhat et al. (Trans. Amer. Math. Soc.370 (2018) 2605–2637), we determine all continuous roots of the vacuum unit 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. Afterwards, we prove that the index of that product system and the Hilbert B- B module of all continuous roots of the vacuum unit are isomorphic as Hilbert two-sided modules.