Bounded and absolutely summing operators between sequence spaces

Abstract

In this thesis, we consider the diagonal operators d_α; α=(α_n) between the sequence l^pspaces, and we give the necessary and sufficient conditions for the diagonal operator to be bounded. Then we give necessary and sufficient conditions for general operators between l^p-spaces to be bounded. Finally, we give a different variation of the stamen of Garling’s Theorem, which gives a complete characterization for diagonal operator d_α between l^p-spaces to be p-absolutely summing, and give an alternative proof for this fundamental theorem.