|
A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices
Author(s):
Lajos
Molnár
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2839-2848.
MSC (2000):
Primary 15A60, 15A15;
Secondary 15A48, 15A57
Posted:
April 11, 2006
Retrieve article in:
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:
-
- 1.
- C.G. Cao, Multiplicative functions of
 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:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org