Some classes of Cesàro-type difference sequences over n-normed spaces

Hemen Dutta

doi:10.1186/1687-1847-2013-286

Abstract

In this paper, we introduce some Cesàro-type difference sequences spaces defined over a real linear n-normed space and investigate the spaces for completeness under suitable n-norm in each case. Relevant relations among the classes of sequences are examined. We also introduce the notion of n-BK-spaces and show that the spaces can be made an n-BK-space under certain condition. Further, we compute the Köthe-Toeplitz duals of the spaces, wherever possible within the scope of the research of this article.MSC:40A05, 46A20, 46D05, 46A45, 46E30.

Highlights

The studies of linear transformation on sequence spaces are called summability
The earliest idea of summability theory was perhaps contained in a letter written by Leibnitz to
Wolf ( ), in which the sum of the oscillatory series - + - + - - - - as given by Leibnitz was Studies on sequence space were further extended through summability theory

Summary

Introduction

The studies of linear transformation on sequence spaces are called summability. The earliest idea of summability theory was perhaps contained in a letter written by Leibnitz toWolf ( ), in which the sum of the oscillatory series - + - + - - - - as given by Leibnitz was Studies on sequence space were further extended through summability theory. The studies of linear transformation on sequence spaces are called summability. The zero element of a normed linear space (n.l.s.) is denoted by θ . A complete n.l.s. is called a Banach space. The space p for p ≥ is complete under the norm defined by x = ( k |xk|p) /p.

Results

Conclusion