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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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000021 |
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| _version_ | 1850169110370975744 |
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| author | Albert Wilansky |
| author_facet | Albert Wilansky |
| author_sort | Albert Wilansky |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-adc47f96d7a74b0b8f8e4eb2e621121d |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-adc47f96d7a74b0b8f8e4eb2e621121d2025-08-20T02:20:49ZengWileyInternational 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. |
| spellingShingle | Albert Wilansky Mazur spaces International Journal of Mathematics and Mathematical Sciences sequentially continuous linear maps classification of compact T2 spaces. |
| title | Mazur spaces |
| title_full | Mazur spaces |
| title_fullStr | Mazur spaces |
| title_full_unstemmed | Mazur spaces |
| title_short | Mazur spaces |
| title_sort | mazur spaces |
| 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 |