1. bookVolume 22 (2014): Issue 4 (December 2014)
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Bidual Spaces and Reflexivity of Real Normed Spaces

Published Online: 31 Dec 2014
Page range: 303 - 311
Received: 29 Nov 2014
Journal Details
License
Format
Journal
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English

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].

Keywords

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