A Urysohn-type theorem and the Bishop-Phelps-Bollobás theorem for holomorphic functions

Sun Kwang Kim; Han Ju Lee

doi:10.1016/j.jmaa.2019.123393

A Urysohn-type theorem and the Bishop-Phelps-Bollobás theorem for holomorphic functions

Sun Kwang Kim
, Han Ju Lee

Department of Mathematics Education

Chungbuk National University

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

7 Scopus citations

Abstract

A Urysohn-type theorem is introduced for a subalgebra of the algebra C_b(Ω) of all bounded complex-valued continuous functions on a Hausdorff topological space Ω. With use of this theorem, it is shown that a type of the Bishop-Phelps-Bollobás theorem holds for certain classes of holomorphic functions on the unit ball of a complex Banach space X if X is either a locally uniformly convex space or a locally c-uniformly convex, order-continuous sequence space.

Original language	English
Article number	123393
Journal	Journal of Mathematical Analysis and Applications
Volume	480
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2019.123393
State	Published - 15 Dec 2019

Keywords

Bishop-Phelps-Bollobás theorem
Holomorphic functions
Peak point
Strong peak points
Uryshon lemma

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10.1016/j.jmaa.2019.123393

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abstract = "A Urysohn-type theorem is introduced for a subalgebra of the algebra Cb(Ω) of all bounded complex-valued continuous functions on a Hausdorff topological space Ω. With use of this theorem, it is shown that a type of the Bishop-Phelps-Bollob{\'a}s theorem holds for certain classes of holomorphic functions on the unit ball of a complex Banach space X if X is either a locally uniformly convex space or a locally c-uniformly convex, order-continuous sequence space.",

keywords = "Bishop-Phelps-Bollob{\'a}s theorem, Holomorphic functions, Peak point, Strong peak points, Uryshon lemma",

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AB - A Urysohn-type theorem is introduced for a subalgebra of the algebra Cb(Ω) of all bounded complex-valued continuous functions on a Hausdorff topological space Ω. With use of this theorem, it is shown that a type of the Bishop-Phelps-Bollobás theorem holds for certain classes of holomorphic functions on the unit ball of a complex Banach space X if X is either a locally uniformly convex space or a locally c-uniformly convex, order-continuous sequence space.

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KW - Peak point

KW - Strong peak points

KW - Uryshon lemma

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M1 - 123393

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A Urysohn-type theorem and the Bishop-Phelps-Bollobás theorem for holomorphic functions

Abstract

Keywords

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