A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices
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- by Lajos Molnár
- Proc. Amer. Math. Soc. 134 (2006), 2839-2848
- DOI: https://doi.org/10.1090/S0002-9939-06-08319-5
- Published electronically: April 11, 2006
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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.References
- Chong Guang Cao, Multiplicative functions of $n\times n$ matrix semigroups over arbitrary fields, J. Math. (Wuhan) 11 (1991), no. 1, 35–38 (Chinese, with English summary). MR 1139669
- Anatolij Dvurečenskij, Gleason’s theorem and its applications, Mathematics and its Applications (East European Series), vol. 60, Kluwer Academic Publishers Group, Dordrecht; Ister Science Press, Bratislava, 1993. MR 1256736, DOI 10.1007/978-94-015-8222-3
- Jiangnan Fan, Determinants and multiplicative functionals on quaternion matrices, Linear Algebra Appl. 369 (2003), 193–201. MR 1988486, DOI 10.1016/S0024-3795(02)00722-X
- Desmond Fearnley-Sander, A characterization of the determinant, Amer. Math. Monthly 82 (1975), no. 8, 838–840. MR 399126, DOI 10.2307/2319807
- R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1996.
- Simon Kochen and E. P. Specker, The problem of hidden variables in quantum mechanics, J. Math. Mech. 17 (1967), 59–87. MR 0219280, DOI 10.1512/iumj.1968.17.17004
- Theodore W. Palmer, Banach algebras and the general theory of $^*$-algebras. Vol. I, Encyclopedia of Mathematics and its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and Banach algebras. MR 1270014, DOI 10.1017/CBO9781107325777
Bibliographic Information
- Lajos Molnár
- Affiliation: Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
- Email: molnarl@math.klte.hu
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2839-2848
- MSC (2000): Primary 15A60, 15A15; Secondary 15A48, 15A57
- DOI: https://doi.org/10.1090/S0002-9939-06-08319-5
- MathSciNet review: 2231606