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Positivity of polarizations of $n$-positive maps

Author: Piotr Kicinski
Journal: Proc. Amer. Math. Soc. 127 (1999), 783-789
MSC (1991): Primary 43A35
MathSciNet review: 1469417
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Abstract: It is shown that polarization formulas have explicit matrix representations. This enables us to prove that polarization formulas of $n$-positive maps between $C^{*}$-algebras are coordinatewise positive.

References [Enhancements On Off] (What's this?)

  • 1. Ando, T., Choi, M.-D., Non-Linear Completely Positive Maps, Aspects of Positivity in Functional Analysis, 1986. MR 88a:46059
  • 2. Takesaki, Masamichi, Theory of Operator Algebras I, Springer-Verlag, New York, Heidelberg, Berlin, 1979. MR 81e:46038
  • 3. Stochel, Jan, Decomposition and Disintegration of Positive Definite Kernels on Convex *-Semigroups, Annales Polonici Mathematici 56 (1992). MR 93g:43003
  • 4. Ando T., Inequalities for permanents, Hokkaido Math. J. 10 (1981). MR 83i:15010
  • 5. Schoenberg, I.J., Positive Definite Functions on Spheres, Duke Math. J. 9 (1942), 96-108. MR 3:232c

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Additional Information

Piotr Kicinski
Affiliation: Instytut Matematyki UJ, ul.Reymonta 4, PL-30059, Krakøw, Poland

Keywords: Completely positive map, polarization of nonlinear map, positive matrix
Received by editor(s): June 20, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society