A QUANTITATIVE VERSION OF JAMES'S COMPACTNESS THEOREM

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10127317" target="_blank" >RIV/00216208:11320/12:10127317 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1017/S0013091510000842" target="_blank" >http://dx.doi.org/10.1017/S0013091510000842</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0013091510000842" target="_blank" >10.1017/S0013091510000842</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A QUANTITATIVE VERSION OF JAMES'S COMPACTNESS THEOREM

Popis výsledku v původním jazyce

We introduce two measures of weak non-compactness Ja_E and Ja that quantify, via distances, the idea of boundary that lies behind James's Compactness Theorem. These measures tell us, for a bounded subset C of a Banach space E and for given x* is an element of E*, how far from E or C one needs to go to find x** in w*-cl(C) with x**(x*) = sup x*(C). A quantitative version of James's Compactness Theorem is proved using Ja_E and Ja, and in particular it yields the following result. Let C be a closed convexbounded subset of a Banach space E and r > 0. If there is an element x_0** in w*-cl(C) whose distance to C is greater than r, then there is x* is an element of E* such that each x** is an element of w*-cl(C) at which sup x*(C) is attained has distance toE greater than 1/2 r. We indeed establish that Ja_E and Ja are equivalent to other measures of weak non-compactness studied in the literature. We also collect particular cases and examples showing when the inequalities between the differ

Název v anglickém jazyce

A QUANTITATIVE VERSION OF JAMES'S COMPACTNESS THEOREM

Popis výsledku anglicky

We introduce two measures of weak non-compactness Ja_E and Ja that quantify, via distances, the idea of boundary that lies behind James's Compactness Theorem. These measures tell us, for a bounded subset C of a Banach space E and for given x* is an element of E*, how far from E or C one needs to go to find x** in w*-cl(C) with x**(x*) = sup x*(C). A quantitative version of James's Compactness Theorem is proved using Ja_E and Ja, and in particular it yields the following result. Let C be a closed convexbounded subset of a Banach space E and r > 0. If there is an element x_0** in w*-cl(C) whose distance to C is greater than r, then there is x* is an element of E* such that each x** is an element of w*-cl(C) at which sup x*(C) is attained has distance toE greater than 1/2 r. We indeed establish that Ja_E and Ja are equivalent to other measures of weak non-compactness studied in the literature. We also collect particular cases and examples showing when the inequalities between the differ

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/IAA100190901" target="_blank" >IAA100190901: Topologické a geometrické struktury v Banachovych prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the Edinburgh Mathematical Society

ISSN

0013-0915

e-ISSN

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Svazek periodika

55

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

18

Strana od-do

369-386

Kód UT WoS článku

000303129100006

EID výsledku v databázi Scopus

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