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Unbounded local completely positive maps of local order zero

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Abstract

We describe the structure of local completely positive maps of local order zero.

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References

  1. Bhat, B.V.R., Ghatak, A., Kumar, P.S.: Stinespring’s theorem for unbounded operator valued local completely positive maps and its application (2020). arXiv:2004.12717

  2. Bhatt, S.J., Karia, D.J.: Complete positivity, tensor products and \(C^{\ast }\)-nuclearity for inverse limits of \(C^{\ast }\)-algebras. Proc. Indian Acad. Sci. Math. Sci. 101(3), 149–167 (1991)

    Article  MathSciNet  Google Scholar 

  3. Dosiev, A.: Local operator spaces, unbounded operators and multinormed \(C^{\ast }\)-algebras. J. Funct. Anal. 255, 1724–1760 (2008)

    Article  MathSciNet  Google Scholar 

  4. Fragoulopoulou, M.: Topological algebras with involution , North-Holland Mathematics Studies, 200. Elsevier Science B.V., Amsterdam. xvi+495 pp. ISBN:0-444-52025-2 (2005)

  5. Gheondea, A.: Operator models for Hilbert locally \( C^{\ast }\)-modules. Oper. Matrices 11(3), 639–667 (2017)

    Article  MathSciNet  Google Scholar 

  6. Inoue, A.: Locally \(C^{\ast }\)-algebras. Mem. Fac. Sci. Kyushu Univ. Ser. A 25, 197–235 (1971)

    MathSciNet  MATH  Google Scholar 

  7. Joiţa, M.: Strict completely positive linear maps between locally \(C^{\ast }\)-algebras and representations on Hilbert modules. J. Lond. Math. Soc. 66(2), 421–432 (2002)

    Article  Google Scholar 

  8. Joiţa, M.: On tensor products of completely positive linear maps between pro-\(C^{\ast }\)-algebras. Positivity 13(2), 307–319 (2009)

    Article  MathSciNet  Google Scholar 

  9. Joiţa, M.: Completely positive maps of order zero on pro-\(C^{\ast }\)-algebras, Forum Math. 33(1), 29–37 (2021)

  10. Karimi, K., Sharifi, K.: Completely positive maps on Hilbert modules over pro-\(C^{\ast }\)-algebras. Bull. Math. Soc. Sci. Math. Roumaine 60(2), 181–193 (2017)

    MathSciNet  MATH  Google Scholar 

  11. Maliev, I.N., Pliev, M.A.: A Stinespring-type representation for operators in Hilbert modules over local \(\mathit{C}^{ \mathit{\ast }}\)-algebras. Russian Math. (Iz. VUZ) 56(12), 43–49; translated from Izv. Vyssh. Uchebn. Zaved. Mat. 12, 51–58 (2012)

  12. Moslehian, M.S., Kusraev, A., Pliev, M.: Matrix KSGNS construction and a Radon-Nikodym type theorem. Indag. Math. (N.S.) 28(5), 938–952 (2017)

    Article  MathSciNet  Google Scholar 

  13. Phillips, N.C.: Inverse limits of \(C^{\ast }\) -algebras. J. Oper. Theory 19(1), 159–195 (1988)

    MathSciNet  MATH  Google Scholar 

  14. Winter, W., Zacharias, J.: Completely positive maps of order zero. Münster J. Math. 2, 311–324 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Wolff, M.: Disjointness preserving operators on \(C^{\ast }\)-algebras. Arch. Math. 62, 248–253 (1994)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author would like to thank the referees for their careful reading and useful comments.

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  1. Department of Mathematics, Faculty of Applied Sciences, University Politehnica of Bucharest, 313 Spl. Independentei, 060042, Bucharest, Romania

    Maria Joiţa

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  1. Maria Joiţa
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Correspondence to Maria Joiţa.

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Joiţa, M. Unbounded local completely positive maps of local order zero. Positivity 25, 1215–1227 (2021). https://doi.org/10.1007/s11117-021-00808-7

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  • DOI: https://doi.org/10.1007/s11117-021-00808-7

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