Norm-attaining functionals need not contain 2-dimensional subspaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Norm-attaining functionals need not contain 2-dimensional subspaces

Popis výsledku v původním jazyce

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&apos;s result.

Název v anglickém jazyce

Norm-attaining functionals need not contain 2-dimensional subspaces

Popis výsledku anglicky

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&apos;s result.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topologické a geometrické vlastnosti Banachových prostorů a operátorových algeber</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

—

Svazek periodika

272

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

918-928

Kód UT WoS článku

000392555200003

EID výsledku v databázi Scopus

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