Abstract:In the present note we introduce tame functionals on Banach algebras. A functional f ∈ A * on a Banach algebra A is tame if the naturally defined linear operator A → A * , a → f • 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) ⊆ Tame(A). We show that tame functionals on l 1 (G) are induced exactly by tame functions (in the sense of topological dynamics) on G fo… Show more
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