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Positivity of polarizations of  -positive maps
Author(s):
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  -positive maps between  -algebras are coordinatewise positive.
References:
- 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
Email:
kicinski@eta.im.uj.edu.pl
DOI:
10.1090/S0002-9939-99-04588-8
PII:
S 0002-9939(99)04588-8
Keywords:
Completely positive map,
polarization of nonlinear map,
positive matrix
Received by editor(s):
June 20, 1997
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1999,
American Mathematical Society
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