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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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1898-9934
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Volume 22, Issue 1

Issues

Dual Spaces and Hahn-Banach Theorem

Keiko Narita / Noboru Endou / Yasunari Shidama
Published Online: 2014-03-30 | DOI: https://doi.org/10.2478/forma-2014-0007

Summary

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].

Keywords: dual space; Hahn-Banach extension

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About the article

Published Online: 2014-03-30


Citation Information: Formalized Mathematics, Volume 22, Issue 1, Pages 69–77, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2014-0007.

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

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[1]
Keiko Narita, Kazuhisa Nakasho, and Yasunari Shidama
Formalized Mathematics, 2017, Volume 25, Number 3

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