Completely positive maps of order zero on pro-𝐶-algebras

Maria Joiţa 1
  • 1 Department of Mathematics, University Politehnica of Bucharest, Faculty of Applied Sciences, Bucharest, Romania
Maria Joiţa
  • Corresponding author
  • Department of Mathematics, Faculty of Applied Sciences, University Politehnica of Bucharest, 313 Spl. Independentei, 060042, Bucharest, Romania
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Abstract

We extend the definition of order zero maps to the setting of pro-C*-algebras and generalize structure theorems of order zero maps between C*-algebras to strongly bounded order zero maps between pro-C-algebras. An application to tensor products is included.

  • [1]

    S. J. Bhatt and D. J. Karia, Complete positivity, tensor products and C * C^{*}-nuclearity for inverse limits of C * C^{*}-algebras, Proc. Indian Acad. Sci. Math. Sci. 101 (1991), no. 3, 149–167.

    • Crossref
    • Export Citation
  • [2]

    M. Fragoulopoulou, Topological Algebras with Involution, North-Holland Math. Stud. 200, Elsevier Science, Amsterdam, 2005.

  • [3]

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

  • [4]

    M. Joiţa, Hilbert Modules over Locally C * {C^{*}}-Algebras, Bucharest University Press, Bucharest, 2006.

  • [5]

    M. Joiţa, Strict completely positive maps between locally C * C^{*}-algebras and representations on Hilbert modules, J. Lond. Math. Soc. (2) 66 (2002), no. 2, 421–432.

    • Crossref
    • Export Citation
  • [6]

    E. C. Lance, Hilbert C * C^{*}-Modules. A Toolkit for Operator Algebraists, London Math. Soc. Lecture Note Ser. 210, Cambridge University, Cambridge, 1995.

  • [7]

    A. Mallios, Topological Algebras. Selected Topics, North-Holland Math. Stud. 124, North-Holland, Amsterdam, 1986.

  • [8]

    N. C. Phillips, Inverse limits of C * C^{*}-algebras, J. Operator Theory 19 (1988), no. 1, 159–195.

  • [9]

    W. Winter, Covering dimension for nuclear C * C^{*}-algebras, J. Funct. Anal. 199 (2003), no. 2, 535–556.

    • Crossref
    • Export Citation
  • [10]

    W. Winter, Covering dimension for nuclear C * C^{*}-algebras. II, Trans. Amer. Math. Soc. 361 (2009), no. 8, 4143–4167.

    • Crossref
    • Export Citation
  • [11]

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

  • [12]

    W. Winter and J. Zacharias, The nuclear dimension of C C^{\ast}-algebras, Adv. Math. 224 (2010), no. 2, 461–498.

    • Crossref
    • Export Citation
  • [13]

    M. Wolff, Disjointness preserving operators on C * C^{*}-algebras, Arch. Math. (Basel) 62 (1994), no. 3, 248–253.

    • Crossref
    • Export Citation
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