On Norms of Completely Positive Maps

  • Stanislaw J. Szarek
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)


King and Ruskai asked whether the norm of a completely positive map acting between Schatten classes of operators is equal to that of its restriction to the real subspace of self-adjoint operators. Proofs have been promptly supplied by Watrous and Audenaert. Here we provide one more proof, in fact of a slightly more general fact, under the (slightly weaker) assumption of 2-positivity. The argument is elementary and self-contained.


Norms of completely positive maps Schatten norms 2-positivity 

Mathematics Subject Classification (2000)

46L07 46N50 47L07 47L20 81P68 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Stanislaw J. Szarek
    • 1
    • 2
  1. 1.Université Pierre et Marie Curie-Paris 6UMR 7586-Institut de MathématiquesParisFrance
  2. 2.Department of MathematicsCase Western Reserve UniversityClevelandUSA

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