The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces

Sun Kwang Kim; Han Ju Lee; Pei Kee Lin

The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces

Sun Kwang Kim
, Han Ju Lee
, Pei Kee Lin

Department of Mathematics Education

Kyonggi University
University of Memphis

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

6 Scopus citations

Abstract

Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobás property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L∞(μ) or complex c₀, and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollobás property.

Original language	English
Pages (from-to)	243-249
Number of pages	7
Journal	Journal of Nonlinear and Convex Analysis
Volume	17
Issue number	2
State	Published - Feb 2016

Keywords

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

Cite this

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title = "The Bishop-Phelps-Bollob{\'a}s property for operators from L∞(μ) to uniformly convex Banach spaces",

abstract = "Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollob{\'a}s property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L∞(μ) or complex c0, and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollob{\'a}s property.",

keywords = "Approximation, Banach space, Bishop-Phelps-Bollob{\'a}s theorem, Norm-attaining operators",

author = "Kim, \{Sun Kwang\} and Lee, \{Han Ju\} and Lin, \{Pei Kee\}",

year = "2016",

month = feb,

language = "English",

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pages = "243--249",

journal = "Journal of Nonlinear and Convex Analysis",

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T1 - The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces

AU - Kim, Sun Kwang

AU - Lee, Han Ju

AU - Lin, Pei Kee

PY - 2016/2

Y1 - 2016/2

N2 - Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobás property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L∞(μ) or complex c0, and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollobás property.

AB - Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobás property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L∞(μ) or complex c0, and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollobás property.

KW - Approximation

KW - Banach space

KW - Bishop-Phelps-Bollobás theorem

KW - Norm-attaining operators

UR - https://www.scopus.com/pages/publications/85055088373

M3 - Article

AN - SCOPUS:85055088373

SN - 1345-4773

VL - 17

SP - 243

EP - 249

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

IS - 2

ER -

The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces

Abstract

Keywords

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