## 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.

### MSC:

 43A07 Means on groups, semigroups, etc.; amenable groups
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### References:

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