Evaluation functions and reflexivity of Banach spaces of holomorphic functions

Guangfu Cao; Li He; Ji Li; Shuqing Zhang

doi:10.1017/S1446788724000077

Evaluation functions and reflexivity of Banach spaces of holomorphic functions

Guangfu Cao, Li He, Ji Li, Shuqing Zhang

School of Mathematical and Physical Sciences

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

Abstract

Let B(Ω) be a Banach space of holomorphic functions on a bounded connected domain Ω in Cⁿ. In this paper, we establish a criterion for B(Ω) to be reflexive via evaluation functions on B(Ω), that is, B(Ω) is reflexive if and only if the evaluation functions span the dual space (B(Ω))^∗.

Original language	English
Pages (from-to)	164-177
Number of pages	14
Journal	Journal of the Australian Mathematical Society
Volume	118
Issue number	2
Early online date	31 May 2024
DOIs	https://doi.org/10.1017/S1446788724000077
Publication status	Published - Apr 2025

Keywords

Banach space of holomorphic functions
evaluation function
reflexivity

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10.1017/S1446788724000077

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title = "Evaluation functions and reflexivity of Banach spaces of holomorphic functions",

abstract = "Let B(Ω) be a Banach space of holomorphic functions on a bounded connected domain Ω in Cn. In this paper, we establish a criterion for B(Ω) to be reflexive via evaluation functions on B(Ω), that is, B(Ω) is reflexive if and only if the evaluation functions span the dual space (B(Ω))∗.",

keywords = "Banach space of holomorphic functions, evaluation function, reflexivity",

author = "Guangfu Cao and Li He and Ji Li and Shuqing Zhang",

year = "2025",

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T1 - Evaluation functions and reflexivity of Banach spaces of holomorphic functions

AU - Cao, Guangfu

AU - He, Li

AU - Li, Ji

AU - Zhang, Shuqing

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Y1 - 2025/4

N2 - Let B(Ω) be a Banach space of holomorphic functions on a bounded connected domain Ω in Cn. In this paper, we establish a criterion for B(Ω) to be reflexive via evaluation functions on B(Ω), that is, B(Ω) is reflexive if and only if the evaluation functions span the dual space (B(Ω))∗.

AB - Let B(Ω) be a Banach space of holomorphic functions on a bounded connected domain Ω in Cn. In this paper, we establish a criterion for B(Ω) to be reflexive via evaluation functions on B(Ω), that is, B(Ω) is reflexive if and only if the evaluation functions span the dual space (B(Ω))∗.

KW - Banach space of holomorphic functions

KW - evaluation function

KW - reflexivity

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UR - http://purl.org/au-research/grants/arc/DP220100285

U2 - 10.1017/S1446788724000077

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EP - 177

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 2

ER -

Evaluation functions and reflexivity of Banach spaces of holomorphic functions

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DP22: Harmonic analysis of Laplacians in curved spaces

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Evaluation functions and reflexivity of Banach spaces of holomorphic functions

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DP22: Harmonic analysis of Laplacians in curved spaces

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