Some results about Beurling algebras with applications to operator theory
Studia Mathematica, Tome 115 (1995) no. 1, pp. 39-52
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $(1-T)^{[β]+1}x ≠ 0$.
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author = {Thomas Vils Pedersen},
title = {Some results about {Beurling} algebras with applications to operator theory},
journal = {Studia Mathematica},
pages = {39--52},
publisher = {mathdoc},
volume = {115},
number = {1},
year = {1995},
doi = {10.4064/sm-115-1-39-52},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-115-1-39-52/}
}
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%0 Journal Article %A Thomas Vils Pedersen %T Some results about Beurling algebras with applications to operator theory %J Studia Mathematica %D 1995 %P 39-52 %V 115 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-115-1-39-52/ %R 10.4064/sm-115-1-39-52 %G en %F 10_4064_sm_115_1_39_52
Thomas Vils Pedersen. Some results about Beurling algebras with applications to operator theory. Studia Mathematica, Tome 115 (1995) no. 1, pp. 39-52. doi: 10.4064/sm-115-1-39-52
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