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Module homomorphisms associated with Banach algebras. (English) Zbl 1231.43002
Let \(A\) be a Banach algebra with the first and second conjugate spaces \(A^* \) and \(A^{**}\) respectively. The author studies operators \(T\) on the dual space \(A\)* and tries to establish conditions when the equality \(T(af) = aT(F)\) (\(a\in A,f\in A^*\)) implies that \(T(Ff)=FT(f)\) (\(f\in A^*, F\in A^{**}\)). He introduces the notion of weakly periodic operators on the dual of a Banach algebra and studies the relationship between almost periodic operators and weakly periodic functionals in \(A^*\).

43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
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