On banach spaces with the approximate hyperplane series property

Yun Sung Choi; Sun Kwang Kim; Han Ju Lee; Miguel Martín

doi:10.15352/bjma/09-4-13

On banach spaces with the approximate hyperplane series property

Yun Sung Choi
, Sun Kwang Kim
, Han Ju Lee
, Miguel Martín

Department of Mathematics Education

Pohang University of Science and Technology
Kyonggi University
University of Granada

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

6 Scopus citations

Abstract

We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollobás version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of w*-continuous operators and other related results.

Original language	English
Pages (from-to)	243-258
Number of pages	16
Journal	Banach Journal of Mathematical Analysis
Volume	9
Issue number	4
DOIs	https://doi.org/10.15352/bjma/09-4-13
State	Published - 2015

Keywords

Approximation
Banach space
Bishop-Phelps-Bollobás theorem
Norm-attaining operators

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10.15352/bjma/09-4-13

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title = "On banach spaces with the approximate hyperplane series property",

abstract = "We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollob{\'a}s version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of w*-continuous operators and other related results.",

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AU - Choi, Yun Sung

AU - Kim, Sun Kwang

AU - Lee, Han Ju

AU - Martín, Miguel

PY - 2015

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N2 - We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollobás version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of w*-continuous operators and other related results.

AB - We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollobás version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of w*-continuous operators and other related results.

KW - Approximation

KW - Banach space

KW - Bishop-Phelps-Bollobás theorem

KW - Norm-attaining operators

UR - https://www.scopus.com/pages/publications/84928090409

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DO - 10.15352/bjma/09-4-13

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VL - 9

SP - 243

EP - 258

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

IS - 4

ER -

On banach spaces with the approximate hyperplane series property

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