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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 $$A^*$$.

##### MSC:
 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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