On the approximate fixed point property in abstract spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10127319" target="_blank" >RIV/00216208:11320/12:10127319 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s00209-011-0915-6" target="_blank" >http://dx.doi.org/10.1007/s00209-011-0915-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00209-011-0915-6" target="_blank" >10.1007/s00209-011-0915-6</a>

Result language

angličtina

Original language name

On the approximate fixed point property in abstract spaces

Original language description

Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X *. In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X *, and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/IAA100190901" target="_blank" >IAA100190901: Topological and geometric structures in Banach spaces</a><br>

Continuities

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

Publication year

2012

Confidentiality

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

Name of the periodical

Mathematische Zeitschrift

ISSN

0025-5874

e-ISSN

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Volume of the periodical

271

Issue of the periodical within the volume

3-4

Country of publishing house

DE - GERMANY

Number of pages

15

Pages from-to

1271-1285

UT code for WoS article

000306342700035

EID of the result in the Scopus database

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