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

Abstract

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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].

How to cite

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Keiko 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 -

References

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Citations in EuDML Documents

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

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