# Dual Spaces and Hahn-Banach Theorem

Keiko Narita; Noboru Endou; Yasunari Shidama

Formalized Mathematics (2014)

- Volume: 22, Issue: 1, page 69-77
- ISSN: 1426-2630

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topKeiko Narita, Noboru Endou, and Yasunari Shidama. "Dual Spaces and Hahn-Banach Theorem." Formalized Mathematics 22.1 (2014): 69-77. <http://eudml.org/doc/266684>.

@article{KeikoNarita2014,

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].},

author = {Keiko Narita, Noboru Endou, Yasunari Shidama},

journal = {Formalized Mathematics},

keywords = {dual space; Hahn-Banach extension},

language = {eng},

number = {1},

pages = {69-77},

title = {Dual Spaces and Hahn-Banach Theorem},

url = {http://eudml.org/doc/266684},

volume = {22},

year = {2014},

}

TY - JOUR

AU - Keiko Narita

AU - Noboru Endou

AU - Yasunari Shidama

TI - Dual Spaces and Hahn-Banach Theorem

JO - Formalized Mathematics

PY - 2014

VL - 22

IS - 1

SP - 69

EP - 77

AB - 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].

LA - eng

KW - dual space; Hahn-Banach extension

UR - http://eudml.org/doc/266684

ER -

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## Citations in EuDML Documents

top- Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama, Topological Properties of Real Normed Space
- Keiko Narita, Noboru Endou, Yasunari Shidama, The Orthogonal Projection and the Riesz Representation Theorem
- Keiko Narita, Noboru Endou, Yasunari Shidama, Bidual Spaces and Reflexivity of Real Normed Spaces
- Kazuhisa Nakasho, Noboru Endou, Separability of Real Normed Spaces and Its Basic Properties
- Keiko Narita, Yasunari Shidama, Noboru Endou, Weak Convergence and Weak Convergence