There is no operatorwise version of the Bishop–Phelps–Bollobás property

Sheldon Dantas; Vladimir Kadets; Sun Kwang Kim; Han Ju Lee; Miguel Martín

doi:10.1080/03081087.2018.1560388

There is no operatorwise version of the Bishop–Phelps–Bollobás property

Sheldon Dantas
, Vladimir Kadets
, Sun Kwang Kim
, Han Ju Lee
, Miguel Martín

Department of Mathematics Education

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

8 Scopus citations

Abstract

Given two real Banach spaces X and Y with dimensions greater than one, it is shown that there is a sequence (Formula presented.) of norm attaining norm-one operators from X to Y and a point (Formula presented.) with (Formula presented.), such that (Formula presented.) This shows that a version of the Bishop–Phelps–Bollobás property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional.

Original language	English
Pages (from-to)	1767-1778
Number of pages	12
Journal	Linear and Multilinear Algebra
Volume	68
Issue number	9
DOIs	https://doi.org/10.1080/03081087.2018.1560388
State	Published - 1 Sep 2020

Keywords

Banach space
Bishop–Phelps–Bollobás property
P. Semrl
norm attaining operators

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10.1080/03081087.2018.1560388

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title = "There is no operatorwise version of the Bishop–Phelps–Bollob{\'a}s property",

abstract = "Given two real Banach spaces X and Y with dimensions greater than one, it is shown that there is a sequence (Formula presented.) of norm attaining norm-one operators from X to Y and a point (Formula presented.) with (Formula presented.), such that (Formula presented.) This shows that a version of the Bishop–Phelps–Bollob{\'a}s property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional.",

keywords = "Banach space, Bishop–Phelps–Bollob{\'a}s property, P. Semrl, norm attaining operators",

author = "Sheldon Dantas and Vladimir Kadets and Kim, \{Sun Kwang\} and Lee, \{Han Ju\} and Miguel Mart{\'i}n",

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T1 - There is no operatorwise version of the Bishop–Phelps–Bollobás property

AU - Dantas, Sheldon

AU - Kadets, Vladimir

AU - Kim, Sun Kwang

AU - Lee, Han Ju

AU - Martín, Miguel

PY - 2020/9/1

Y1 - 2020/9/1

N2 - Given two real Banach spaces X and Y with dimensions greater than one, it is shown that there is a sequence (Formula presented.) of norm attaining norm-one operators from X to Y and a point (Formula presented.) with (Formula presented.), such that (Formula presented.) This shows that a version of the Bishop–Phelps–Bollobás property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional.

AB - Given two real Banach spaces X and Y with dimensions greater than one, it is shown that there is a sequence (Formula presented.) of norm attaining norm-one operators from X to Y and a point (Formula presented.) with (Formula presented.), such that (Formula presented.) This shows that a version of the Bishop–Phelps–Bollobás property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional.

KW - Banach space

KW - Bishop–Phelps–Bollobás property

KW - P. Semrl

KW - norm attaining operators

UR - https://www.scopus.com/pages/publications/85059322328

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DO - 10.1080/03081087.2018.1560388

M3 - Article

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 9

ER -

There is no operatorwise version of the Bishop–Phelps–Bollobás property

Abstract

Keywords

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