Ordered involutive operator spaces

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)497-510
Number of pages14
Issue number3
StatePublished - Aug 2007
Externally publishedYes


  • C*- envelope
  • Loewner order
  • Noncommutative Shilov boundary
  • Operator spaces
  • Operator system
  • Positive operator
  • Unitization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Analysis
  • General Mathematics


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