A NEW SEQUENCE SPACE AND NORM OF CERTAIN MATRIX OPERATORS ON THIS SPACE

In the present paper, we introduce the sequence space l(p) (E, Delta) = {x = (x(n))(n=1)(infinity) : Sigma(infinity)(n=1) vertical bar Sigma(j is an element of En) x(j) - Sigma(j is an element of En+1) x(j)vertical bar(p) < infinity}, where E = (E-n) is a partition of finite subsets of the positive integers and p >= 1. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from l(p) into l(p)(E, Delta), and apply our results to Copson and Hilbert matrices.