Strong Ditkin algebras without bounded relative units

Abstract

In a previous note the author gave an example of a strong Ditkin algebra which does not have bounded relative units in the sense of Dales. In this note we investigate a certain family of Banach function algebras on the one point compactification of ℕ, and see that within this family are many easier examples of strong Ditkin algebras without bounded relative units in the sense of Dales.

Keywords

• Banach function algebras
• functional analysis
• strong Ditkin algebras
• bounded relative units.