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

Cyril Agrafeuil

Studia Mathematica, Tome 166 (2005), p. 133-151 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Détail

Publié le : 2005-01-01

Zbl 1081.46033

EUDML-ID : urn:eudml:doc:284392