, Volume 11, Issue 3, pp 497-510

Ordered Involutive Operator Spaces

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Abstract

This is a companion to recent papers of the authors; here we construct the ‘noncommutative Shilov boundary’ of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider ‘maximal’ and ‘minimal’ unitizations of such ordered operator spaces.

Blecher was partially supported by grant DMS 0400731 from the National Science Foundation. Kirkpatrick was partially supported by an NSF REU grant. Neal was supported by Denison University. Werner was supported by the SFB 487 Geometrische Strukturen in der Mathematik, at the Westfälische Wilhelms-Universität, supported by the Deutsche Forschungsgemeinschaft.