Pseudo-characters and almost multiplicative functionals. (English) Zbl 0958.43001

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.


43A07 Means on groups, semigroups, etc.; amenable groups
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