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)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-06-08319-5
Published electronically: April 11, 2006
MathSciNet review: 2231606
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • 1. C.G. Cao, Multiplicative functions of $ n\times n$ matrix semigroups over arbitrary fields, J. Math. (Wuhan) 11 (1991), 35-38. MR 1139669 (92k:20122)
  • 2. A. Dvurecenskij, Gleason's Theorem and Its Applications, Kluwer Academic Publishers, 1993. MR 1256736 (94m:46092)
  • 3. J. Fan, Determinants and multiplicative functionals on quaternion matrices, Linear Algebra Appl. 369 (2003), 193-201. MR 1988486 (2004c:15007)
  • 4. D. Fearnley-Sander, A characterization of the determinant, Amer. Math. Monthly 82 (1975), 838-840. MR 0399126 (53:2977)
  • 5. R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1996.
  • 6. 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)
  • 7. 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 15A60, 15A15, 15A48, 15A57

Retrieve articles in all journals with MSC (2000): 15A60, 15A15, 15A48, 15A57


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: https://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.

American Mathematical Society