Skip to main content
SpringerLink
Log in

Representation of completely positive maps between partial *-algebras

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 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.

    MathSciNet  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • Ekhaguere, G. O. S. (1988). Dirichlet forms on partial *-algebras,Mathematical Proceedings of the Cambridge Philosophical Society,104, 129–140.

    MATH  MathSciNet  Google Scholar 

  • Ekhaguere, G. O. S. (1993). Noncommutative mean ergodic theorem on partial *-algebras,International Journal of Theoretical Physics,32, 1187–1196.

    Article  MATH  MathSciNet  Google Scholar 

  • Ekhaguere, G. O. S., and Odiobala, P. O. (1991). Completely positive conjugate-bilinear maps on partial *-algebras,Journal of Mathematical Physics,32, 2951–2958.

    Article  ADS  MathSciNet  Google Scholar 

  • Lassner, G., and Lassner, G. A. (1977). Completely positive mappings and unbounded observables,Reports on Mathematical Physics,11, 133–140.

    MathSciNet  Google Scholar 

  • Paschke, W. L. (1973). Inner product modules overB*-algebras,Transactions of the American Mathematical Society,182, 443–468.

    MATH  MathSciNet  Google Scholar 

  • Powers, R. T. (1974). Self-adjoint algebras of unbounded operators II,Transactions of the American Mathematical Society,187, 261–293.

    MATH  MathSciNet  Google Scholar 

  • Stinespring, W. T. (1955). Positive functions onC*-algebras,Proceedings of the American Mathematical Society,6, 211–216.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. G. O. S. Ekhaguere

    Present address: Department of Mathematics, University of Ibadan, Ibadan, Nigeria

Authors and Affiliations

  1. International Centre for Theoretical Physics, P.O. Box 586, I-34100, Trieste, Italy

    G. O. S. Ekhaguere

Authors
  1. G. O. S. Ekhaguere
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ekhaguere, G.O.S. Representation of completely positive maps between partial *-algebras. Int J Theor Phys 35, 1571–1580 (1996). https://doi.org/10.1007/BF02302259

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02302259

Keywords

Search

Navigation