Additive units of product system of Hilbert modules

Abstract

In this paper we consider the notion of additive units and roots of a central unital unit in a spatial product system of two-sided Hilbert C*-modules. This is a generalization of the notion of additive units and roots of a unit in a spatial product system of Hilbert spaces introduced in [B. V. R. Bhat, M. Lindsay, M. Mukherjee, Additive units of product system, arXiv:1501.07675v1 [math.FA] 30 Jan 2015]. We introduce the notion of continuous additive unit and continuous root of a central unital unit ω in a spatial product system over C*-algebra B and prove that the set of all continuous additive units of ω can be endowed with a structure of two-sided Hilbert B - B module wherein the set of all continuous roots of ω is a Hilbert B - B submodule.