Taiwanese Journal of Mathematics

$N$-JORDAN $*$-HOMOMORPHISMS IN $C^{*}$-ALGEBRAS

Choonkil Park, Shahram Ghaffary Ghaleh, and Khatereh Ghasemi

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Abstract

In this paper, we investigate $n$-Jordan $*$-homomorphisms in $C^{*}$-algebras associated with the following functional inequality $$\left\|f\left(\frac{b-a}{3} \right) + f\left( \frac{a-3c}{3} \right) + f\left( \frac{3a+3c-b}{3} \right)\right\|\leq \|f(a)\|.$$ We moreover prove the superstability and the Hyers-Ulam stability of $n$-Jordan $*$-homomorphisms in $C^{*}$-algebras associated with the following functional equation $$f\left( \frac{b-a}{3} \right) + f\left( \frac{a-3c}{3} \right) + f\left(\frac{3a+3c-b}{3} \right) = f(a).$$

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1803-1814.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406798

Digital Object Identifier
doi:10.11650/twjm/1500406798

Mathematical Reviews number (MathSciNet)
MR2970686

Zentralblatt MATH identifier
1382.39044

Subjects
Primary: 17C65: Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 39B52: Equations for functions with more general domains and/or ranges 39B72: Systems of functional equations and inequalities 46L05: General theory of $C^*$-algebras

Keywords
$n$-Jordan $*$-homomorphism $C^{*}$-algebra Hyers-Ulam stability

Citation

Park, Choonkil; Ghaleh, Shahram Ghaffary; Ghasemi, Khatereh. $N$-JORDAN $*$-HOMOMORPHISMS IN $C^{*}$-ALGEBRAS. Taiwanese J. Math. 16 (2012), no. 5, 1803--1814. doi:10.11650/twjm/1500406798. https://projecteuclid.org/euclid.twjm/1500406798


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