# Ordered Involutive Operator Spaces

## Authors

Article

- Received:
- Accepted:

DOI: 10.1007/s11117-007-2086-6

- Cite this article as:
- Blecher, D.P., Kirkpatrick, K., Neal, M. et al. Positivity (2007) 11: 497. doi:10.1007/s11117-007-2086-6

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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.

### Mathematics Subject Classification (2000)

Primary 47L0747L05Secondary 46B4046L0746L0847B6047B65### Keywords

Positive operatorLoewner orderoperator spacesoperator systemunitizationnoncommutative Shilov boundaryC*- envelope## Copyright information

© Birkhäuser Verlag, Basel 2007