ALAMT  Vol.3 No.2 , June 2013
Jordan Semi-Triple Multiplicative Maps on the Symmetric Matrices
ABSTRACT

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


Cite this paper
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.
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.

 
 
Top