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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
Posted:
April 11, 2006
MathSciNet review:
2231606
Full-text PDF Free Access
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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.
References
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C.G. Cao, Multiplicative functions of
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A. Dvurecenskij, Gleason's Theorem and Its Applications, Kluwer Academic Publishers, 1993. MR 1256736 (94m:46092)
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J. Fan, Determinants and multiplicative functionals on quaternion matrices, Linear Algebra Appl. 369 (2003), 193-201. MR 1988486 (2004c:15007)
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D. Fearnley-Sander, A characterization of the determinant, Amer. Math. Monthly 82 (1975), 838-840. MR 0399126 (53:2977)
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R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1996.
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S. Kochen and E.P. Specker, The problem of hidden variables in quantum mechanics, J. Math. Mech. 17 (1967), 59-87. MR 0219280 (36:2363)
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T.W. Palmer, Banach Algebras and The General Theory of *-Algebras, Vol. I, Encyclopedia Math. Appl. 49, Cambridge University Press, 1994. MR 1270014 (95c:46002)
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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
Posted:
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 after
28 years from publication.
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