On the block sequence space lp(E) and related matrix transformations

Abstract

The purpose of the present study is to introduce the sequence space lp(E) = {x = (xn)∞n=1 :∑∞n=1 ∑ j∈En xjp < ∞ } , where E = (En) is a partition of finite subsets of the positive integers and 1 ≤ p < ∞. We investigate some topological properties of this space and also give some inclusion relations concerning it. Furthermore, we compute α- and β -duals of this space and characterize the matrix transformations from the space lp(E) to the space X , where X ∈ {l∞, c, c0}. Key words: Sequence spaces, matrix domains, α- and β -duals, matrix transformations