Spectral synthesis in regular Banach algebras

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Abstract

We prove that every locally compact non-discrete abelian group G contains a compact subset E such that A(E) - the restriction algebra of A(G) to E - admits spectral synthesis, although it contains a closed, regular, self-adjoint subalgebra which is isomorphic to an algebra of infinitely differentiable functions on [-1, 1]. We also give some general results concerning the failure of spectral synthesis in regular Banach algebras.

Original languageEnglish
Pages (from-to)197-212
Number of pages16
JournalIsrael Journal of Mathematics
Volume8
Issue number3
DOIs
StatePublished - Sep 1970

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