Pseudo-characters and almost multiplicative functionals
The main subject studied in the paper under review is the so called stable approximability of the set of characters or continuous characters on a group, i.e. the question whether they can uniformly on \(G\) approximate every almost character. Theorem 1 asserts that on an amenable locally compact group every measurable \(\varepsilon\)-character can uniformly be approximated on \(G\) by continuous characters. The logarithms of multiplicative pseudo-characters can be chosen to be some real additive almost characters (Theorem 2) and in Theorem 3 the author shows that the involutive Banach group algebra \(\ell_1(G)\) is an AMNM (i.e. ``algebra on which almost multiplicative functionals are near to multiplicative functionals'') if and only if the set of characters on \(G\) is stable.
scientific article; zbMATH DE number 1506534
scientific article