Reflexivity of linear n-normed space with respect to b-linear functional

TL;DR

This paper explores the reflexivity of linear n-normed spaces concerning bounded b-linear functionals, extending the Hahn-Banach theorem and analyzing convergence concepts within this framework.

Contribution

It introduces the notion of reflexivity in linear n-normed spaces relative to bounded b-linear functionals and discusses convergence properties.

Findings

Reflexivity of linear n-normed spaces is characterized with respect to bounded b-linear functionals.

Properties of strong and weak convergence in linear n-normed spaces are established.

Extensions of the Hahn-Banach theorem for bounded b-linear functionals are discussed.

Abstract

In continuation of the paper [3], we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of reflexivity of linear n-normed space with respect to bounded b-linear functional. The concepts of strong convergence and weak convergence of a sequence of vectors with respect to bounded b-linear functionals in linear n-normed space have been introduced and some of their properties are being discussed.