Approximate jordan mappings on noncommutative banach algebras

Commun. Korean Math. Soc. 1997 Vol. 12, No. 1, 69-73

Young Whan Lee, Gwang Hui Kim Taejon University, kangnam University

Abstract : We show that if $T$ is an $\varepsilon -$approximate Jordan functional such that $T(a) = 0$ implies $T(a^2 )=0\ (a \in A)$ then $T$ is continuous and $\Vert T \Vert \le 1+ \varepsilon $. Also we prove that every $\varepsilon -$near Jordan mapping is an $g(\varepsilon )-$approximate Jordan mapping where $g(\varepsilon ) \to 0$ as $ \varepsilon \to 0$ and for every $\varepsilon >0$ there is an integer $m$ such that if $T$ is an $ \frac {\varepsilon }{m} -$approximate Jordan mapping on a finite dimensional Banach algebra then $T$ is an $\varepsilon -$near Jordan mapping.

Keywords : Approximate Jordan mapping, Banach algebra