  In the present note we introduce tame functionals on Banach algebras. A
functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined
linear operator $A \to A^*, a \mapsto f \cdot a$ factors through Rosenthal
Banach spaces (i.e., not containing a copy of $l_1$). Replacing Rosenthal by
reflexive we get a well known concept of weakly almost periodic functionals.
So, always $WAP(A) \subseteq Tame(A)$. We show that tame functionals on the
group algebra $l_1(G)$ are induced exactly by tame functions (in the sense of
topological dynamics) on $G$ for every discrete group $G$. That is,
$Tame(l_1(G))=Tame(G)$. Many interesting tame functions on groups come from
dynamical systems theory. Recall that $WAP(L_1(G))=WAP(G)$ (Lau 1977, \"{U}lger
1986) for every locally compact group $G$. It is an open question if
$Tame(L_1(G))=Tame(G)$ holds for (nondiscrete) locally compact groups.
