On Isomorphism in C*-Ternary Algebras for a Cauchy-Jensen Functional Equations

R.Murali; K.Ravi; N.Anbumani

doi:https://doi.org/10.14445/22315373/IJMTT-V8P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 8 | Number 2 | Year 2014 | Article Id. IJMTT-V8P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V8P512

On Isomorphism in C*-Ternary Algebras for a Cauchy-Jensen Functional Equations

R.Murali, K.Ravi , N.Anbumani

Abstract

In this paper, we investigate isomorphisms between C*-ternary algebras by proving the Hyers-Ulam-Rassias stability of homomorphisms in * C -ternary algebras and of derivations on C*-ternary algebras for the following Cauchy-Jensen additive mapping:

Keywords

Cauchy-Jensen functional equation, C*-ternary algebra isomorphism, Hyers- Ulam-Rassias stability, C*-ternary derivation

References

[1] C. Baak, Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces, Act Math, Sinica, in Press.
[2] Choonkil, Abbas najati, Cauchy-Jensen additive mappings in quasi-banach algebras and its applica- tions, ISPACS (2013).
[3] Z. Gajda, On stability of additive mappings, Int. J .Math. Math. Sci. 14 (1991) 431-434.
[4] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184(1994) 431-436.
[5] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941) 222-224.
[6] D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in several variables, Birkhauser, Basel, 1998.
[7] M.S. Moslehian, Almost derivation on C∗-ternary rings, Preprint.
[8] C. Park, Homomorphisms between Poisson JC∗-algebras, Bull. Braz. Math. Soc. 36 (2005) 79-97.
[9] C. Park, Isomorphisms between C∗-ternary algebras, J. Math Anal. Appl. 327 (2007) 101-115.
[10] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Amer. Math. Soc. 72(1978) 297-300.
[11] Th.M. Rassias, P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, proc. Amer. Math. Soc. 114 (1992) 989-993.
[12] J.M. Rassias, H.M. Kim, Approximate homomorphisms and derivations between C∗-ternary algebras, J. Math. Phys. 49 (2008), no.6, 10pp.
[13] S.M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964 (2.Chapter VI, Some Questions in Analysis: 1, Stability).
[14] H. Zettl, A characterization of ternary rings of operators, Adv. Math. 48 (1983) 117-143.

Citation :

R.Murali, K.Ravi , N.Anbumani, "On Isomorphism in C*-Ternary Algebras for a Cauchy-Jensen Functional Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 8, no. 2, pp. 83-94, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V8P512