Advertisement

International Journal of Theoretical Physics

, Volume 35, Issue 8, pp 1571–1580 | Cite as

Representation of completely positive maps between partial *-algebras

  • G. O. S. Ekhaguere
Article

Abstract

A characterization of the invariant completely positive conjugate-bilinear maps from an arbitrary partial *-algebra to a semiassociative, locally convex partial *-algebra is given. The result generalizes Stinespring's characterization of completely positive maps onC*-algebras, as well as its recent extensions by a number of authors.

Keywords

Field Theory Elementary Particle Quantum Field Theory Recent Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antoine, J.-P., and Inoue, A. (1990). Representability of invariant positive sesquilinear forms on partial *-algebras,Mathematical Proceedings of the Cambridge Philosophical Society,108, 337–353.MathSciNetGoogle Scholar
  2. Antoine, J.-P., Inoue, A., and Trapani, C. (1990). Partial *-algebras of closable operators I. Basic theory and the abelian case,Publications RIMS, Kyoto University,26, 359–395.MathSciNetGoogle Scholar
  3. Antoine, J.-P., Inoue, A., and Trapani, C. (1991). Partial *-algebras of closable operators II. States and representations of partial *-algebras,Publications RIMS, Kyoto University,27, 399–430.MathSciNetGoogle Scholar
  4. Ekhaguere, G. O. S. (1988). Dirichlet forms on partial *-algebras,Mathematical Proceedings of the Cambridge Philosophical Society,104, 129–140.MATHMathSciNetGoogle Scholar
  5. Ekhaguere, G. O. S. (1993). Noncommutative mean ergodic theorem on partial *-algebras,International Journal of Theoretical Physics,32, 1187–1196.CrossRefMATHMathSciNetGoogle Scholar
  6. Ekhaguere, G. O. S., and Odiobala, P. O. (1991). Completely positive conjugate-bilinear maps on partial *-algebras,Journal of Mathematical Physics,32, 2951–2958.CrossRefADSMathSciNetGoogle Scholar
  7. Lassner, G., and Lassner, G. A. (1977). Completely positive mappings and unbounded observables,Reports on Mathematical Physics,11, 133–140.MathSciNetGoogle Scholar
  8. Paschke, W. L. (1973). Inner product modules overB*-algebras,Transactions of the American Mathematical Society,182, 443–468.MATHMathSciNetGoogle Scholar
  9. Powers, R. T. (1974). Self-adjoint algebras of unbounded operators II,Transactions of the American Mathematical Society,187, 261–293.MATHMathSciNetGoogle Scholar
  10. Stinespring, W. T. (1955). Positive functions onC*-algebras,Proceedings of the American Mathematical Society,6, 211–216.MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • G. O. S. Ekhaguere
    • 1
  1. 1.International Centre for Theoretical PhysicsTriesteItaly

Personalised recommendations