The norm of certain matrix operators on the new difference sequence spaces I

The purpose of the present study is to introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. 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,Delta)$ is investigated.