A Duality Theorem for Real C* Algebras

  • M. Andrew Moshier
  • Daniela Petrişan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5728)


The full subcategory of proximity lattices equipped with some additional structure (a certain form of negation) is equivalent to the category of compact Hausdorff spaces. Using the Stone-Gelfand-Naimark duality, we know that the category of proximity lattices with negation is dually equivalent to the category of real C * algebras. The aim of this paper is to give a new proof for this duality, avoiding the construction of spaces. We prove that the category of C * algebras is equivalent to the category of skew frames with negation, which appears in the work of Moshier and Jung on the bitopological nature of Stone duality.


Rational Number Commutative Ring Duality Theorem Full Subcategory Information Order 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Andrew Moshier
    • 1
  • Daniela Petrişan
    • 2
  1. 1.Department of Mathematics and Computer ScienceChapman UniversityUSA
  2. 2.Department of Computer ScienceUniversity of LeicesterUK

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