Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions

Colin Bennett; John E. Gilbert

Annales de l'institut Fourier (1972)

  • Volume: 22, Issue: 3, page 21-50
  • ISSN: 0373-0956

Abstract

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This paper considers the Lipschitz subalgebras Λ ( α , p , 𝒜 ) of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in Λ ( α , p ; 𝒜 ) , α ≠ [ α ] . From these estimates the Ditkin and Analytic Ditkin conditions for Λ ( α , p ; 𝒜 ) follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to Λ ( α ; , p ; 𝒜 ) as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed showing that many of the Banach algebras on the circle considered previously in isolation can be both generated and describes within this framework of interpolation space theory.

How to cite

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Bennett, Colin, and Gilbert, John E.. "Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions." Annales de l'institut Fourier 22.3 (1972): 21-50. <http://eudml.org/doc/74089>.

@article{Bennett1972,
abstract = {This paper considers the Lipschitz subalgebras $\Lambda (\alpha ,p,\{\cal A\})$ of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in $\Lambda (\alpha ,p;\{\cal A\})$, $\alpha \ne [\alpha ]$. From these estimates the Ditkin and Analytic Ditkin conditions for $\Lambda (\alpha ,p;\{\cal A\})$ follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to $\Lambda (\alpha ;,p;\{\cal A\})$ as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed showing that many of the Banach algebras on the circle considered previously in isolation can be both generated and describes within this framework of interpolation space theory.},
author = {Bennett, Colin, Gilbert, John E.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {21-50},
publisher = {Association des Annales de l'Institut Fourier},
title = {Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions},
url = {http://eudml.org/doc/74089},
volume = {22},
year = {1972},
}

TY - JOUR
AU - Bennett, Colin
AU - Gilbert, John E.
TI - Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions
JO - Annales de l'institut Fourier
PY - 1972
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 3
SP - 21
EP - 50
AB - This paper considers the Lipschitz subalgebras $\Lambda (\alpha ,p,{\cal A})$ of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in $\Lambda (\alpha ,p;{\cal A})$, $\alpha \ne [\alpha ]$. From these estimates the Ditkin and Analytic Ditkin conditions for $\Lambda (\alpha ,p;{\cal A})$ follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to $\Lambda (\alpha ;,p;{\cal A})$ as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed showing that many of the Banach algebras on the circle considered previously in isolation can be both generated and describes within this framework of interpolation space theory.
LA - eng
UR - http://eudml.org/doc/74089
ER -

References

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