, Volume 11, Issue 3, pp 497–510

Ordered Involutive Operator Spaces

  • David P. Blecher
  • Kay Kirkpatrick
  • Matthew Neal
  • Wend Werner

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


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


Positive operatorLoewner orderoperator spacesoperator systemunitizationnoncommutative Shilov boundaryC*- envelope

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  • David P. Blecher
    • 1
  • Kay Kirkpatrick
    • 2
  • Matthew Neal
    • 3
  • Wend Werner
    • 4
  1. 1.Department of MathematicsUniversity of HoustonHouston
  2. 2.Department of MathematicsMITCambridge
  3. 3.Department of MathematicsDenison UniversityGranville
  4. 4.Mathematisches InstitutMünsterGermany