Dual Spaces and Hahn-Banach Theorem
In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition...
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Sciendo
2014-03-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.2478/forma-2014-0007 |
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doaj-933244d0ef754b5bbd3095fcb2c581d52021-09-05T21:01:03ZengSciendoFormalized Mathematics1898-99342014-03-01221697710.2478/forma-2014-0007Dual Spaces and Hahn-Banach TheoremNarita Keiko0Endou Noboru1Shidama Yasunari2Hirosaki-city Aomori, JapanGifu National College of Technology Gifu, JapanShinshu University Nagano, JapanIn this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved the Hahn-Banach extension theorem in real normed spaces. We have used extensively used [17].https://doi.org/10.2478/forma-2014-0007dual spacehahn-banach extension |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Narita Keiko Endou Noboru Shidama Yasunari |
| spellingShingle |
Narita Keiko Endou Noboru Shidama Yasunari Dual Spaces and Hahn-Banach Theorem Formalized Mathematics dual space hahn-banach extension |
| author_facet |
Narita Keiko Endou Noboru Shidama Yasunari |
| author_sort |
Narita Keiko |
| title |
Dual Spaces and Hahn-Banach Theorem |
| title_short |
Dual Spaces and Hahn-Banach Theorem |
| title_full |
Dual Spaces and Hahn-Banach Theorem |
| title_fullStr |
Dual Spaces and Hahn-Banach Theorem |
| title_full_unstemmed |
Dual Spaces and Hahn-Banach Theorem |
| title_sort |
dual spaces and hahn-banach theorem |
| publisher |
Sciendo |
| series |
Formalized Mathematics |
| issn |
1898-9934 |
| publishDate |
2014-03-01 |
| description |
In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved the Hahn-Banach extension theorem in real normed spaces. We have used extensively used [17]. |
| topic |
dual space hahn-banach extension |
| url |
https://doi.org/10.2478/forma-2014-0007 |
| work_keys_str_mv |
AT naritakeiko dualspacesandhahnbanachtheorem AT endounoboru dualspacesandhahnbanachtheorem AT shidamayasunari dualspacesandhahnbanachtheorem |
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1717781734480674816 |