Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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. 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
  • 2. Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
  • 3. Jan Stochel, Decomposition and disintegration of positive definite kernels on convex *-semigroups, Ann. Polon. Math. 56 (1992), no. 3, 243–294. MR 1160416
  • 4. Tsuyoshi Ando, Inequalities for permanents, Hokkaido Math. J. 10 (1981), no. Special Issue, 18–36. MR 662295
  • 5. Schoenberg, I.J., Positive Definite Functions on Spheres, Duke Math. J. 9 (1942), 96-108. MR 3:232c

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A35

Retrieve articles in all journals with MSC (1991): 43A35

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