Some results about Beurling algebras with applications to operator theory

Thomas Vils Pedersen

Studia Mathematica (1995)

  • Volume: 115, Issue: 1, page 39-52
  • ISSN: 0039-3223

Abstract

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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 .

How to cite

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Vils Pedersen, Thomas. "Some results about Beurling algebras with applications to operator theory." Studia Mathematica 115.1 (1995): 39-52. <http://eudml.org/doc/216197>.

@article{VilsPedersen1995,
author = {Vils Pedersen, Thomas},
journal = {Studia Mathematica},
keywords = {power bounded operator; maximal ideals in Beurling algebras on the unit disc; approximate identities},
language = {eng},
number = {1},
pages = {39-52},
title = {Some results about Beurling algebras with applications to operator theory},
url = {http://eudml.org/doc/216197},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Vils Pedersen, Thomas
TI - Some results about Beurling algebras with applications to operator theory
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 1
SP - 39
EP - 52
LA - eng
KW - power bounded operator; maximal ideals in Beurling algebras on the unit disc; approximate identities
UR - http://eudml.org/doc/216197
ER -

References

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