Dual Spaces and Hahn-Banach Theorem

• Autorzy: Keiko Narita , Noboru Endou , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

dual space; Hahn-Banach extension

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 1
• Strony: 69-77

Twórcy

autor

Keiko Narita

• Hirosaki-city Aomori, Japan

autor

Noboru Endou

• Gifu National College of Technology Gifu, Japan

autor

Yasunari Shidama

• Shinshu University Nagano, Japan

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Identyfikatory

DOI

10.2478/forma-2014-0007