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

Prasenjit Ghosh, Tapas Kumar Samanta

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.

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

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.

Paper Structure

This paper contains 5 sections, 100 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Consequences of Hahn-Banach theorem in linear $n$-normed space
  4. Reflexivity of linear $n$-normed space
  5. $b$-weak convergence and $b$-strong convergence in linear $n$-normed space

Theorems & Definitions (16)

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