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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The minimum norm of certain completely positive maps


Author: Ching Yun Suen
Journal: Proc. Amer. Math. Soc. 123 (1995), 2407-2416
MSC: Primary 46L05; Secondary 47D25
DOI: https://doi.org/10.1090/S0002-9939-1995-1213870-2
MathSciNet review: 1213870
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Abstract: Let L be a completely bounded linear map from a unital $ {C^ \ast }$-algebra to the algebra of all bounded linear operators on a Hilbert space. Then

$\displaystyle \min \left\{ {{{\left\Vert \phi \right\Vert}_{{\text{cb}}}}:{{\le... ...ve}}} \hfill \\ {{\text{for all}}\;n} \hfill \\ \end{array} } \right\} = 2S(L),$

where $ S(L) = \min \{ {\left\Vert \phi \right\Vert _{{\text{cb}}}}:\phi \pm \operatorname{Re} \lambda L$ is completely positive for all $ \vert\lambda \vert = 1\} $.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1213870-2
Keywords: Completely positive map, completely bounded map, numerical radius
Article copyright: © Copyright 1995 American Mathematical Society