Jordan Semi-Triple Multiplicative Maps on the  Symmetric Matrices

Xiaoning Hao; Pengxiang Ren; Runling An

doi:10.4236/alamt.2013.32003

Home > Journals > Physics & Mathematics > ALAMT

Advances in Linear Algebra & Matrix Theo... > Vol.3 No.2, June 2013

Jordan Semi-Triple Multiplicative Maps on the Symmetric Matrices ()

Department of Mathematics, Taiyuan University of Technology, Staff Education and Training Center of Taiyuan Iron and Steel (Group) Co., Ltd., Taiyuan, China.

DOI: 10.4236/alamt.2013.32003 PDF HTML XML 2,875 Downloads 6,729 Views Citations

Abstract

In this paper, we show that if an injective map on symmetric matrices S_n(C) satisfies
then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and A_f is the image of A under f applied entrywise.

Keywords

Symmetric Matrices; Orthogonal Matrix; Jordan Homomorphism

Share and Cite:

X. Hao, P. Ren and R. An, "Jordan Semi-Triple Multiplicative Maps on the Symmetric Matrices," Advances in Linear Algebra & Matrix Theory, Vol. 3 No. 2, 2013, pp. 11-16. doi: 10.4236/alamt.2013.32003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. S. Matindale III, “When Are Multiplicative Mappings Additive?” Proceedings of the American Mathematical Society, Vol. 21, No. 3, 1969, pp. 695-698. doi:10.1090/S0002-9939-1969-0240129-7
[2]	P. ?emrl, “Isomorphisms of Standard Operator Algebras,” Proceedings of the American Mathematical Society, Vol. 123, No. 6, 1995, pp. 1851-1855.
[3]	L. Molnár, “On Isomorphisms of Standard Operator Algebras,” Studia Mathematica, Vol. 142, 2000, pp. 295-302.
[4]	J. Hakeda, “Additivity of -Semigroup Isomorphisms among -Algebra,” Bulletin of the London Mathematical Society, Vol. 18, No. 1, 1986, pp. 51-56. doi:10.1112/blms/18.1.51
[5]	L. Molnár, “Jordan Maps on Standard Operator Algebras,” In: Z. Daroczy and Z. Páles, Eds., Functional Equations-Results and Advances, Kulwer Academic Publishers.
[6]	F. Lu, “Additivity of Jordan Maps on Standard Operator Algebras,” Linear Algebra and its Applications, Vol. 357, No. 1-3, 2002, pp. 123-131. doi:10.1016/S0024-3795(02)00367-1
[7]	R. L. An and J. C. Hou, “Additivity of Jordan Multiplicative Maps on Jordan Operator Algebras,” Taiwanese journal of mathematics, Vol. 10, No. 1, 2006, pp. 45-64.