CONTINUITY OF AN APPROXIMATE JORDAN MAPPING

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

File

Download PDF

References

1. J. A. Baker, The stability o] the cDsine equations, Proc. Amer. Math. Soc. 80 (1980),411-416 https://doi.org/10.2307/2043730
2. F. F. BonsaI and J. Duncan, Complete stormed algebras, Springer-Verlag, Berlin, 1973
3. K. Jarosz, Purturbaiions o] Banach algebras, Lecture Notes in mathematics, Springer-Verlag, Berlin 1120 (1985)
4. B. E. Johnson, Approximatelt Multiplicative maps between Banach algebras, J. London Math. Soc. 31 (1988), no. 2, 294-316
5. Y. W. Lee and G. H. Kim, Continuity and super stability of Jordan mappings, Studia Univ, Babes-Bolyai Mathematica, XLVII (2002), no. 1,61-66