Reflexivity of a Banach Space with a Countable Vector Space Basis

TL;DR

This paper presents a specific criterion for determining the reflexivity of Banach spaces that possess a countable vector space basis, enhancing understanding of their duality properties.

Contribution

It introduces a new criterion for reflexivity in Banach spaces with a countable basis, linking basis properties to reflexivity.

Findings

Reflexivity is linked to the properties of the countable basis.

A new criterion for reflexivity is established.

Applicable to classical function and sequence spaces.

Abstract

All most all the function spaces over real or complex domains and spaces of sequences, that arise in practice as examples of normed complete linear spaces (Banach spaces), are reflexive. These Banach spaces are dual to their respective spaces of continuous linear functionals over the corresponding Banach spaces. For each of these Banach spaces, a countable vector space basis exists, which is responsible for their reflexivity. In this paper, a specific criterion for reflexivity of a Banach space with a countable vector space basis is presented.