The sequence space bv and some applications

TL;DR

This paper explores the properties, dual spaces, and matrix transformations of the sequence space bv, introduces its matrix domain with various means, and characterizes related matrix classes.

Contribution

It introduces the matrix domain of bv with different means and computes duals, providing new insights into the structure of these sequence spaces.

Findings

Computed alpha-, beta-, gamma-duals of the spaces

Characterized matrix classes of the new spaces

Analyzed properties and duals of the sequence space bv

Abstract

In this work, we give well-known results related to some properties, dual spaces and matrix transformations of the sequence space bv and introduce the matrix domain of space bv with arbitrary triangle matrix A. Afterward, we choose the matrix A as Ces\`aro mean of order one, generalized weighted mean and Riesz mean and compute alpha-; beta- gamma-duals of these spaces. And also, we characterize the matrix classes of the new spaces.