THE NORM OF CERTAIN MATRIX OPERATORS ON NEW DIFFERENCE SEQUENCE SPACES

The purpose of the present study is to introduce the sequence space lp(Δ;E) ={ x = (xn)∞ n=1 :∑∞ n=1|xminEn - xminEn+1| p ∞ } ; where E = (En) 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 lp into lp(Δ;E) is investigated.