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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
##### Keywords:
local operator; hyper-Tauberian algebra; Tauberian algebra
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##### References:
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