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Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary
Agrafeuil, Cyril
Zarrabi, Mohamed (Université Bordeaux I. Laboratoire Bordelais d'Analyse et de Géométrie)

Data: 2008
Resum: We denote by T the unit circle and by D the unit disc. Let B be a semi-simple unital commutative Banach algebra of functions holomorphic in D and continuous on D, endowed with the pointwise product. We assume that B is continously imbedded in the disc algebra and satisfies the following conditions: (H1) The space of polynomials is a dense subset of B. (H2) limn→+∞ kz nk1/nB = 1. (H3) There exist k ≥ 0 and C > 0 such that˛˛1 − ˛k‚‚f‚‚B ≤ C‚‚(z − λ)f‚‚B, (f ∈ B, < 2). When B satisfies in addition the analytic Ditkin condition, we give a complete characterisation of closed ideals I of B with countable hull h(I), where h(I) = ˘z ∈ D : f(z) = 0, (f ∈ I)¯. Then, we apply this result to many algebras for which the structure of all closed ideals is unknown. We consider, in particular, the weighted algebras ℓ1(ω) and L1(R+, ω).
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Closed ideals ; Banach algebras ; Ditkin condition
Publicat a: Publicacions Matemàtiques, V. 52 n. 1 (2008) p. 19-56, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_52108_02

38 p, 338.0 KB

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