Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

• Autorzy: Cyril Agrafeuil
• Języki publikacji: FR EN

Abstrakty

EN

We denote by 𝕋 the unit circle and by 𝔻 the unit disc of ℂ. Let s be a non-negative real and ω a weight such that $ω(n) = (1 + n)^{s}$ (n ≥ 0) and the sequence $(ω(-n)/(1+n)^{s})_{n≥0}$ is non-decreasing. We define the Banach algebra
$A_{ω}(𝕋) = {f ∈ 𝓒(𝕋): ||f||_{ω} = ∑_{n=-∞}^{+∞} |f̂(n)|ω(n) < +∞ }$.
If I is a closed ideal of $A_{ω}(𝕋)$, we set $h⁰(I) = {z ∈ 𝕋: f(z) = 0 (f ∈ I)}$. We describe all closed ideals I of $A_{ω}(𝕋)$ such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra $A⁺_{s}(𝕋) = {f ∈ A_{ω}(𝕋): f̂(n) = 0 (n < 0)}$ without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating sets for $𝑎^{∞}$, the space of infinitely differentiable functions in the closed unit disc 𝔻̅ and holomorphic in 𝔻.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 46J20: Ideals, maximal ideals, boundaries
• 30H05: Bounded analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 167
• Numer: 2
• Strony: 133-151

Daty

wydano

2005

Twórcy

autor

Cyril Agrafeuil

• Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, France

Identyfikatory

DOI

10.4064/sm167-2-2