There is no operatorwise version of the Bishop-Phelps-Bollobas property

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00346270" target="_blank" >RIV/68407700:21230/20:00346270 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1080/03081087.2018.1560388" target="_blank" >https://doi.org/10.1080/03081087.2018.1560388</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03081087.2018.1560388" target="_blank" >10.1080/03081087.2018.1560388</a>

Result language
angličtina
Original language name
There is no operatorwise version of the Bishop-Phelps-Bollobas property
Original language description
Given two real Banach spacesXandYwith dimensions greater than one, it is shown that there is a sequence{Tn}n is an element of Nof norm attaining norm-one operators fromXtoYand a pointx0 is an element of Xwith parallel to x0 parallel to=1, such that parallel to Tn(x0)parallel to 1 but infn is an element of N{dist(x0,{x is an element of X:parallel to Tn(x)parallel to=parallel to x parallel to=1})}>0.This shows that a version of the Bishop-Phelps-Bollobas property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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