The Norm of Certain Matrix Operators on New Difference Sequence Spaces

Abstract

The purpose of the present study is to introduce the sequence space

 l_p(∆,E) = { x = (x_n)^∞ _n=1 : ∑^∞ _n=1 |x_minEn - x_minEn+1| ^p < ∞}.

where E = (E_n) is a partition of finite subsets of the positive integers and p ≥1. The topological properties and inclusion relations of this space are studied. Moreover, the problem of finding the norm of certain matrix operators such as Copson and Hilbert from l_p into l_p (∆,E) is investigated.

Key words and phrases. Difference sequence space, matrix domains, norm, Copson matrix, Hilbert matrix.

2000 Mathematics Subject Classification. 46A45, 46B20, 40C05, 40G05