Some results about Beurling algebras with applications to operator theory
Studia Mathematica, Tome 115 (1995) no. 1, p. 39.

Voir la notice de l'article dans European Digital Mathematics Library

We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying ∥ T n ∥ = O ( n β ) as n → ∞ for some β ≥ 0, then ∑ n = 1 ∞ ∥ ( 1 - T ) n x ∥ / ∥ ( 1 - T ) n - 1 x ∥ diverges for every x ∈ X such that ( 1 - T ) [ β ] + 1 x ≠ 0 .
Classification : 47A30, 43A15, 46J15, 46J20
Mots-clés : power bounded operator, maximal ideals in Beurling algebras on the unit disc, approximate identities 
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Thomas Vils Pedersen. Some results about Beurling algebras with applications to operator theory. Studia Mathematica, Tome 115 (1995) no. 1, p. 39. https://geodesic-test.mathdoc.fr/item/STUMA_1995__115_1_216197/