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 | References | Similar Articles | Additional Information

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

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.