Interpolating sequences on uniform algebras

Pablo Galindo; Mikael Lindström; Alejandro Miralles

doi:10.1016/j.top.2009.11.009

Interpolating sequences on uniform algebras

Pablo Galindo, Mikael Lindström, Alejandro Miralles^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

4 Citations (Scopus)

Abstract

We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of c₀, then it is sufficient for any dual uniform algebra.

Original language	English
Pages (from-to)	111-118
Number of pages	8
Journal	Topology
Volume	48
Issue number	2-4
DOIs	https://doi.org/10.1016/j.top.2009.11.009
Publication status	Published - Jun 2009
MoE publication type	A1 Journal article-refereed

Keywords

Analytic function
Interpolating sequence
Pseudohyperbolic distance
Uniform algebra

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10.1016/j.top.2009.11.009

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title = "Interpolating sequences on uniform algebras",

abstract = "We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of c0, then it is sufficient for any dual uniform algebra.",

keywords = "Analytic function, Interpolating sequence, Pseudohyperbolic distance, Uniform algebra",

author = "Pablo Galindo and Mikael Lindstr{\"o}m and Alejandro Miralles",

note = "Funding Information: Supported by Project MTM 2007-064521 (MEC-FEDER, Spain). Alejandro Miralles was also supported by the Juan de la Cierva programme (MICINN, Spain). ",

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AU - Lindström, Mikael

AU - Miralles, Alejandro

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Y1 - 2009/6

N2 - We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of c0, then it is sufficient for any dual uniform algebra.

AB - We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of c0, then it is sufficient for any dual uniform algebra.

KW - Analytic function

KW - Interpolating sequence

KW - Pseudohyperbolic distance

KW - Uniform algebra

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EP - 118

JO - Topology

JF - Topology

IS - 2-4

ER -

Interpolating sequences on uniform algebras

Abstract

Keywords

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