Communications of the
Korean Mathematical Society CKMS

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

MSC numbers: 46H40, 46J10