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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices


Author: Lajos Molnár
Journal: Proc. Amer. Math. Soc. 134 (2006), 2839-2848
MSC (2000): Primary 15A60, 15A15; Secondary 15A48, 15A57
Published electronically: April 11, 2006
MathSciNet review: 2231606
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Abstract: In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.


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Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
Email: molnarl@math.klte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08319-5
PII: S 0002-9939(06)08319-5
Keywords: Positive definite matrices, positive semi-definite matrices, Hermitian matrices, Kochen-Specker theorem, determinant, Jordan triple product
Received by editor(s): February 9, 2005
Received by editor(s) in revised form: April 26, 2005
Published electronically: April 11, 2006
Additional Notes: The author was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T043080, T046203, and by a joint Hungarian-Slovene grant (Reg. No. SLO-10/03).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.