On the Pointwise Bishop-Phelps-Bollobas Property for Operators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00338240" target="_blank" >RIV/68407700:21230/19:00338240 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4153/S0008414X18000032" target="_blank" >https://doi.org/10.4153/S0008414X18000032</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4153/S0008414X18000032" target="_blank" >10.4153/S0008414X18000032</a>
Alternative languages
Result language
angličtina
Original language name
On the Pointwise Bishop-Phelps-Bollobas Property for Operators
Original language description
We study approximation of operators between Banach spaces X and Y that nearly attain their norms in a given point by operators that attain their norms at the same point. When such approximations exist, we say that the pair (X, Y) has the pointwise Bishop-Phelps-Bollobas property (pointwise BPB property for short). In this paper we mostly concentrate on those X, called universal pointwise BPB domain spaces, such that (X, Y) possesses pointwise BPB property for every Y, and on those Y, called universal pointwise BPB range spaces, such that (X, Y) enjoys pointwise BPB property for every uniformly smooth X. We show that every universal pointwise BPB domain space is uniformly convex and that L-p(mu) spaces fail to have this property when p > 2. No universal pointwise BPB range space can be simultaneously uniformly convex and uniformly smooth unless its dimension is one. We also discuss a version of the pointwise BPB property for compact operators.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Canadian Journal of Mathematics
ISSN
0008-414X
e-ISSN
1496-4279
Volume of the periodical
71
Issue of the periodical within the volume
6
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
1421-1443
UT code for WoS article
000496552800006
EID of the result in the Scopus database
2-s2.0-85059301782