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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- Lajos Molnár
- Affiliation: Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
- Email: email@example.com
- 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