Norm-attaining functionals need not contain 2-dimensional subspaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10368178" target="_blank" >RIV/00216208:11320/17:10368178 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2016.10.028" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2016.10.028</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2016.10.028" target="_blank" >10.1016/j.jfa.2016.10.028</a>
Alternative languages
Result language
angličtina
Original language name
Norm-attaining functionals need not contain 2-dimensional subspaces
Original language description
G. Godefroy asked whether, on any Banach space, the set of norm-attaining functionals contains a 2-dimensional linear subspace. We prove that a construction due to C.J. Read provides an example of a space which does not have this property. Read found an equivalent norm (sic) center dot (sic) on c(0) such that (co, (sic) center dot (sic)) contains no proximinal subspaces of codimension 2. Our result is obtained through a study of the relation between the following two sentences, in which X is a Banach space and Y subset of X is a closed subspace: (A) Y is proximinal in X, and (B) Y-perpendicular to consists of norm-attaining functionals. We prove that these are equivalent if X is the space (c(0), (sic) center dot (sic) )and our main theorem then follows as a corollary to Read's result.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Functional Analysis
ISSN
0022-1236
e-ISSN
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Volume of the periodical
272
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
918-928
UT code for WoS article
000392555200003
EID of the result in the Scopus database
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