Pseudocharacters on free semigroups invariant with respect to their automorphism groups

Faĭziev, V.

doi:10.1090/S0002-9939-98-04110-0

Pseudocharacters on free semigroups invariant with respect to their automorphism groups
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Proc. Amer. Math. Soc. 126 (1998), 333-342 Request permission

Abstract:

Let $\mathcal {F}$ be a free semigroup and let $A$ be an automorphism group of $\mathcal {F}$. A description is given of the space of real functions $\varphi$ on semigroup $\mathcal {F}$ satisfying the following conditions: 1) the set $\{\varphi (xy)-\varphi (x)-\varphi (y); x,y\in \mathcal {F} \}$ is bounded; 2) $\varphi (x^{n}) = n\varphi (x)$ for any $x\in \mathcal {F}$ and $n\in N$; 3) $\varphi (x^{\tau }) = \varphi (x) \quad \forall x\in \mathcal {F}$, and $\forall \tau \in A$.

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