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.
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.
[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.