Interpolating sequences for Banach spaces of holomorphic functions

This work studies interpolating sequences for Banach spaces of analytic functions, such as Hardy spaces of bounded holomorphic functions on domains of $\C^N$. New results are obtained on minimal sets of bounded sequences whose interpolation by functions in $H^\infty(\D)$ guarantees that a sequence is interpolating for such spaces. The first sufficient condition, in terms of the Gleason distance, is also provided for a sequence in $M_A \cap X$ to be interpolating for a dual uniform algebra $A = X^*$, together with a simple characterization of interpolating sequences for those bidual uniform algebras that are regular.

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Publication Details

Journal
Repositori UJI (Universitat Jaume I)
Published
2026-02-12
Primary Topic
Advanced Banach Space Theory
Type
article
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article

Interpolating sequences for Banach spaces of holomorphic functions

Mario Pérez Maletzki
Repositori UJI (Universitat Jaume I)
Advanced Banach Space Theory
article

Interpolating sequences for Banach spaces of holomorphic functions

Mario Pérez Maletzki
article en

Abstract

This work studies interpolating sequences for Banach spaces of analytic functions, such as Hardy spaces of bounded holomorphic functions on domains of $\C^N$. New results are obtained on minimal sets of bounded sequences whose interpolation by functions in $H^\infty(\D)$ guarantees that a sequence is interpolating for such spaces. The first sufficient condition, in terms of the Gleason distance, is also provided for a sequence in $M_A \cap X$ to be interpolating for a dual uniform algebra $A = X^*$, together with a simple characterization of interpolating sequences for those bidual uniform algebras that are regular.

Repositori UJI (Universitat Jaume I)
Openalex Percentile: Top 46%
Advanced Banach Space Theory
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Interpolating sequences for Banach spaces of holomorphic functions — Mario Pérez Maletzki · Repositori UJI (Universitat Jaume I) (2026) | TGRS Research Map | TGRS