Commun. Korean Math. Soc. 2005 Vol. 20, No. 3, 505-509 Printed September 1, 2005
Young Whan Lee Daejeon University
Abstract : We show that every $\varepsilon$-approximate Jordan functional on a Banach algebra $A$ is continuous. From this result we obtain that every $\varepsilon$-approximate Jordan mapping from $A$ into a continuous function space $C(S)$ is continuous and it's norm less than or equal $1+\varepsilon$ where $S$ is a compact Hausdorff space. This is a generalization of Jarosz's result [3, Proposition 5.5].
Keywords : Banach algebra, automatic continuity, Jordan mapping, super stability, approximate mapping