On some properties of new paranormed sequence space defined by λ 2 -convergent sequences

Naim L Braha

doi:10.1186/1029-242x-2014-273

Abstract

In this paper, we introduce the new sequence space l( λ 2 ,p) and we will show some topological properties like completeness, isomorphism, and some inclusion relations between this sequence spaces and some of the other sequence spaces. In addition we will compute the α-, β-, and γ-duals of these spaces. At the end of the article we will show some matrix transformations between the l( λ 2 ,p) space and the other spaces.MSC:46A45.

Highlights

By w we denote the space of all complex sequences
For an arbitrary sequence space X, the matrix domain of an infinite matrix A in X is defined by XA = {x ∈ w : Ax ∈ X}, ( )
We introduce the new sequence space l(λ, p) and we will show some topological properties as completeness, isomorphism, and some inclusion relations between this sequence spaces and some of the other sequence spaces

Summary

Introduction

By w we denote the space of all complex sequences. We shall write l , c, and c for the sequence spaces of all bounded, convergent, and null sequences, respectively. We write bs, cs, and cs for the sequence spaces of all bounded, convergent, and null series, respectively. The α-, β-, and γ -duals of a sequence space X are, respectively, defined by

Results

Conclusion