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- W2095340392 abstract "In this paper we study the question whether certain non-semisimple, commutative Banach algebras have a Wedderburn decomposition U = B ⊕ rad U , where B is a subalgebra of U . Let A ( G ) be the Fourier algebra of a locally compact abelian group G , and let E be a closed subset of G . Let J(E) be the smallest closed ideal in A ( G ) whose hull is E . We prove that, when E is a set of non-synthesis, the quotient algebra A(G) J(E) never has a Wedderburn decomposition even in the purely algebraic sense. This result is extended to cover certain Beurling algebras A x ( R k ) and A x ( T k )." @default.
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- W2095340392 date "1992-07-01" @default.
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- W2095340392 title "The Wedderburn decomposability of some commutative Banach algebras" @default.
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- W2095340392 doi "https://doi.org/10.1016/0022-1236(92)90102-o" @default.
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