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http://hdl.handle.net/11320/3726
Tytuł: | Bidual Spaces and Reflexivity of Real Normed Spaces |
Autorzy: | Narita, Keiko Endou, Noboru Shidama, Yasunari |
Słowa kluczowe: | continuous dual space topological duality reflexivity |
Data wydania: | 2014 |
Data dodania: | 9-gru-2015 |
Wydawca: | De Gruyter Open |
Źródło: | Formalized Mathematics, Volume 22, Issue 4, 2014, Pages 303-311 |
Abstrakt: | In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals as linear operators by this definition. Accordingly we proved Uniform Boundedness Theorem for linear functionals using the theorem (5) from [21]. Finally, we defined reflexivity of real normed spaces and proved some theorems about isomorphism of linear operators. Using them, we proved some properties about reflexivity. These formalizations are based on [19], [20], [8] and [1]. |
Afiliacja: | Narita Keiko - Hirosaki-city Aomori, Japan Endou Noboru - Gifu National College of Technology Gifu, Japan Shidama Yasunari - Shinshu University Nagano, Japan |
URI: | http://hdl.handle.net/11320/3726 |
DOI: | 10.2478/forma-2014-0030 |
ISSN: | 1426-2630 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2014, Volume 22, Issue 4 |
Pliki w tej pozycji:
Plik | Opis | Rozmiar | Format | |
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forma-2014-0030.pdf | 259,83 kB | Adobe PDF | Otwórz |
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