<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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].</p></abstract>

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].

Bidual Spaces and Reflexivity of Real Normed Spaces

Gifu National College of Technology Gifu, Japan

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

{"article-title":"Bidual Spaces and Reflexivity of Real Normed Spaces"}

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...

Bidual Spaces and Reflexivity of Real Normed Spaces

Publié en ligne: 31 déc. 2014

Pages: 303 - 311

Reçu: 29 nov. 2014

DOI: https://doi.org/10.2478/forma-2014-0030

Mots clés
continuous dual space, topological duality, reflexivity

© by Keiko Narita

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Bidual Spaces and Reflexivity of Real Normed Spaces

Publié en ligne: 31 déc. 2014

Pages: 303 - 311

Reçu: 29 nov. 2014

DOI: https://doi.org/10.2478/forma-2014-0030

Mots cléscontinuous dual space, topological duality, reflexivity

© by Keiko Narita

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Mots clés
continuous dual space, topological duality, reflexivity