On Analytical Review of Conjugate and Reflexive Spaces

Main Article Content

Eziokwu, C. Emmanuel

Abstract

In this review, we started by considering a normed space , its dual and bi-dual spaces. We define functionals on , as those functionals that are bounded linear functionals and then establish a corresponding unique bounded linear functional that defines a canonical mapping of  into  such that is linear, injective and preserves norm. By this, isomorphism is established so that reflexive maps are realized. In the cause of this work, we invoked the idea of compact topological space and operators mapped on them. We also discussed separable spaces as it relates to this topic. The work was rounded up in section three by discussing the Tychonoff’s theorem as it relates to the weak topology in conjugate spaces, adjoint operators and conjugate spaces of  and .

Keywords:
Normal space, dual space, functional, reflexive space, conjugate space, isomorphism.

Article Details

How to Cite
C. Emmanuel, E. (2020). On Analytical Review of Conjugate and Reflexive Spaces. Asian Research Journal of Current Science, 2(1), 14-27. Retrieved from http://globalpresshub.com/index.php/ARJOCS/article/view/804
Section
Review Article

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