Positivity

, Volume 11, Issue 3, pp 497–510 | Cite as

Ordered Involutive Operator Spaces

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

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 47L07 47L05 Secondary 46B40 46L07 46L08 47B60 47B65 

Keywords

Positive operator Loewner order operator spaces operator system unitization noncommutative Shilov boundary C*- envelope 

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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

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