Mazur spaces

Mazur spaces

A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads...

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Bibliographic Details
Main Author: Albert Wilansky
Format: Article
Language:English
Published: Hindawi Limited 1981-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
sequentially continuous linear maps
classification of compact T2 spaces.
Online Access:http://dx.doi.org/10.1155/S0161171281000021
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spelling doaj-adc47f96d7a74b0b8f8e4eb2e621121d2020-11-24T23:09:09ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-0141395310.1155/S0161171281000021Mazur spacesAlbert Wilansky0Department of Mathematics #14, Lehigh University, Bethlehem 18015, Pennsylvania, USAA Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H) is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball is settled: the dual space need not be Mazur.http://dx.doi.org/10.1155/S0161171281000021sequentially continuous linear mapsclassification of compact T2 spaces.
collection DOAJ
language English
format Article
sources DOAJ
author Albert Wilansky
spellingShingle Albert Wilansky
Mazur spaces
International Journal of Mathematics and Mathematical Sciences
sequentially continuous linear maps
classification of compact T2 spaces.
author_facet Albert Wilansky
author_sort Albert Wilansky
title Mazur spaces
title_short Mazur spaces
title_full Mazur spaces
title_fullStr Mazur spaces
title_full_unstemmed Mazur spaces
title_sort mazur spaces
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 1981-01-01
description A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H) is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball is settled: the dual space need not be Mazur.
topic sequentially continuous linear maps
classification of compact T2 spaces.
url http://dx.doi.org/10.1155/S0161171281000021
work_keys_str_mv AT albertwilansky mazurspaces
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