Positivity of polarizations of $n$-positive maps
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- by Piotr Kiciński PDF
- Proc. Amer. Math. Soc. 127 (1999), 783-789 Request permission
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
- T. Ando and M. D. Choi, Nonlinear completely positive maps, Aspects of positivity in functional analysis (Tübingen, 1985) North-Holland Math. Stud., vol. 122, North-Holland, Amsterdam, 1986, pp. 3–13. MR 859714
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728, DOI 10.1007/978-1-4612-6188-9
- Jan Stochel, Decomposition and disintegration of positive definite kernels on convex $*$-semigroups, Ann. Polon. Math. 56 (1992), no. 3, 243–294. MR 1160416, DOI 10.4064/ap-56-3-243-294
- Tsuyoshi Ando, Inequalities for permanents, Hokkaido Math. J. 10 (1981), no. Special Issue, 18–36. MR 662295
- Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
Additional Information
- Piotr Kiciński
- Affiliation: Instytut Matematyki UJ, ul.Reymonta 4, PL-30059, Krakøw, Poland
- Email: kicinski@eta.im.uj.edu.pl
- Received by editor(s): June 20, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 783-789
- MSC (1991): Primary 43A35
- DOI: https://doi.org/10.1090/S0002-9939-99-04588-8
- MathSciNet review: 1469417