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].
@article{bwmeta1.element.doi-10_2478_forma-2014-0007,
author = {Keiko Narita and Noboru Endou and Yasunari Shidama},
title = {Dual Spaces and Hahn-Banach Theorem},
journal = {Formalized Mathematics},
volume = {22},
year = {2014},
pages = {69-77},
zbl = {1298.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0007}
}
Keiko Narita; Noboru Endou; Yasunari Shidama. Dual Spaces and Hahn-Banach Theorem. Formalized Mathematics, Tome 22 (2014) pp. 69-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0007/
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