The Bishop-Phelps-Bollobas Property and Absolute Sums

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00333042" target="_blank" >RIV/68407700:21230/19:00333042 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00009-019-1346-6" target="_blank" >https://doi.org/10.1007/s00009-019-1346-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00009-019-1346-6" target="_blank" >10.1007/s00009-019-1346-6</a>

Result language
angličtina
Original language name
The Bishop-Phelps-Bollobas Property and Absolute Sums
Original language description
In this paper, we study conditions assuring that the Bishop-Phelps-Bollobas property (BPBp, for short) is inherited by absolute summands of the range space or of the domain space. Concretely, given a pair (X,Y) of Banach spaces having the BPBp, if Y1 is an absolute summand of Y, then (X,Y1) has the BPBp;if X1 is an absolute summand of X of type 1 or , then (X1,Y) has the BPBp. Besides, analogous results for the BPBp for compact operators and for the density of norm-attaining operators are also given. We also show that the Bishop-Phelps-Bollobas property for numerical radius is inherited by absolute summands of type 1 or . Moreover, we provide analogous results for numerical radius attaining operators and for the BPBp for numerical radius for compact operators.
Czech name
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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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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