Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces
In order to study the conditions for bounded closed and convex sets to have a unique completion inreal Banach spaces，known results in this direction are summarized. Based on this，a sufficient condition as well as some necessary and sufficient conditions for bounded closed and convex sets to have a u...
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| Format: | Article |
| Language: | zho |
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Harbin University of Science and Technology Publications
2017-06-01
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| Series: | Journal of Harbin University of Science and Technology |
| Subjects: |
| _version_ | 1818389746832900096 |
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| author | JI Dong-hai GAO Yue-jie |
| author_facet | JI Dong-hai GAO Yue-jie |
| author_sort | JI Dong-hai |
| collection | DOAJ |
| description | In order to study the conditions for bounded closed and convex sets to have a unique completion inreal Banach spaces，known results in this direction are summarized. Based on this，a sufficient condition as well as some necessary and sufficient conditions for bounded closed and convex sets to have a unique completion areprovided. The notion of ( K，u) -completeness is extended，and the relation of this notion to the uniqueness of completion in real Banach spaces is discussed. |
| first_indexed | 2024-12-14T04:46:38Z |
| format | Article |
| id | doaj.art-08037566a9354274af6faa16a31aa773 |
| institution | Directory Open Access Journal |
| issn | 1007-2683 |
| language | zho |
| last_indexed | 2024-12-14T04:46:38Z |
| publishDate | 2017-06-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj.art-08037566a9354274af6faa16a31aa7732022-12-21T23:16:39ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832017-06-0112112610. 15938 /j. jhust. 2017. 03. 022Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach SpacesJI Dong-haiGAO Yue-jie In order to study the conditions for bounded closed and convex sets to have a unique completion inreal Banach spaces，known results in this direction are summarized. Based on this，a sufficient condition as well as some necessary and sufficient conditions for bounded closed and convex sets to have a unique completion areprovided. The notion of ( K，u) -completeness is extended，and the relation of this notion to the uniqueness of completion in real Banach spaces is discussed.( K; u) -completeness; completion of sets; bounded closed and convex sets |
| spellingShingle | JI Dong-hai GAO Yue-jie Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces Journal of Harbin University of Science and Technology ( K; u) -completeness; completion of sets; bounded closed and convex sets |
| title | Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces |
| title_full | Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces |
| title_fullStr | Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces |
| title_full_unstemmed | Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces |
| title_short | Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces |
| title_sort | conditions for bounded closed and convex sets to have a unique completion in banach spaces |
| topic | ( K; u) -completeness; completion of sets; bounded closed and convex sets |
| work_keys_str_mv | AT jidonghai conditionsforboundedclosedandconvexsetstohaveauniquecompletioninbanachspaces AT gaoyuejie conditionsforboundedclosedandconvexsetstohaveauniquecompletioninbanachspaces |