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Hyper-Tauberian algebras defined by a Banach algebra homomorphism. (English) Zbl 07314660
Summary: Let \(A\) and \(B\) be Banach algebras and \(T:B\longrightarrow A\) be a continuous homomorphism. We consider left multipliers from \(A\times_T B\) into its the first dual i.e., \(A^*\times B^*\) and we show that \(A\times_T B\) is a hyper-Tauberian algebra if and only if \(A\) and \(B\) are hyper-Tauberian algebras.
MSC:
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
16W20 Automorphisms and endomorphisms
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