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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 (n ≥ 0) and the sequence is non-decreasing. We define the Banach algebra
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If I is a closed ideal of , we set . We describe all closed ideals I of such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating sets...
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