Abstract
Here we prove an analog of the Stinespring’s theorem for n-tuples of completely positive maps in Hilbert C ⋆-modules.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Stinespring, F. “Positive Functions on C ⋆-Algebras,” Proc. Amer. Math. Soc. 6, No. 2, 211–216 (1955).
Heo, J. “Completely Multi-Positive Linear Maps and Representations on Hilbert C ⋆-Modules,” J. Operator Theory 41, No. 1, 3–22 (1999).
Asadi, M. B. “Stinespring’s Theorem for Hilbert C ⋆-Modules,” J. Operator Theory 62 (2), 235–238 (2009).
Bhat, R., Ramesh, G., Sumesh, K. “Stinespring’s Theorem for Maps on Hilbert C ⋆-Modules,” J. Operator Theory 68, No. 1, 173–178 (2012).
Skeide, M. “A Factorization Theorem for φ-Maps,” J. Operator Theory 68, No. 2, 543–547 (2012).
Joita, M. “Covariant Version of the Stinespring Type Theorem for Hilbert C ⋆-Modules,” Cent. Eur. J. Math. 9, No. 4, 803–813 (2011).
Joita, M. “Comparision of Completely Positive Maps on HilbertC ⋆-Modules,” Preprint, arXiv: 1201.0593v1.
Maliev, I. N., Pliev, M. A. “A Stinespring Type Representation for Opertators in Hilbert Modules Over Local C ⋆-Algebras,” Russian Mathematics (Iz. VUZ) 56, No. 12, 43–49 (2012).
Manuilov, V. M., Troitskii, E. V. C ⋆ -Hilbert Modules (Moscow, Faktorial, 2001) [in Russian].
Murphy G. C ⋆ -Algebras and Operator Theory (Academic Press, 1990; Moscow, Faktorial, 1997).
Lance, E. C. Hilbert C ⋆ -Modules. A Toolkit for Operator Algebraists (Cambridge University Press, 1995).
Paulsen, V. Completly Bounded Maps and Operator Algebras (Cambridge University Press, 2002).
Joita, M. Completely Positive Linear Maps on Pro-C ⋆ -Algebras (University of Bucharest Press, 2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.A. Pliev, I.D. Tsopanov, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 11, pp. 42–49.
About this article
Cite this article
Pliev, M.A., Tsopanov, I.D. On representation of Stinespring’s type for n-tuples of completely positive maps in Hilbert C ⋆-modules. Russ Math. 58, 36–42 (2014). https://doi.org/10.3103/S1066369X1411005X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X1411005X