##### Title: Additive Units of Product System of Hilbert Modules

##### Pages: 71-76

##### Cite as:

Biljana Vujosevic, Additive Units of Product System of Hilbert Modules, Int. J. Anal. Appl., 10 (2) (2016), 71-76.#### 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.

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#### References

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