<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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].</p></abstract>

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].

Dual Spaces and Hahn-Banach Theorem

Gifu National College of Technology Gifu, Japan

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

{"article-title":"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...

Dual Spaces and Hahn-Banach Theorem

Published Online: Mar 30, 2014

Page range: 69 - 77

DOI: https://doi.org/10.2478/forma-2014-0007

Keywords
dual space, Hahn-Banach extension

© by Keiko Narita

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Dual Spaces and Hahn-Banach Theorem

Published Online: Mar 30, 2014

Page range: 69 - 77

DOI: https://doi.org/10.2478/forma-2014-0007

Keywordsdual space, Hahn-Banach extension

© by Keiko Narita

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Keywords
dual space, Hahn-Banach extension