Compact and weakly compact Derivations on l^1(Z_+)
In this thesis, we aim to study derivations from l^1(Z+) to its dual, l^\infty(Z+). We first characterize them as certain closed subspace of l^1(Z+). Then we present a necessary and sufficient condition, due to M. J. Heath, to make a bounded derivation on l^1(Z+) into l^\infty(Z+), a compact linear operator. After that base on the work in , we study weakly compact derivations from l^1(Z+) to its dual. We introduce T-sets and TF-sets and then state their relation with weakly compact operators on l^1(Z+). These results are originally due to Y. Choi and M. J. Heath, but we give simpler proofs. Finally, we will study certain classes of derivations from L^1(R+) to L^\infty(R+), and give an elementary proof that they are always mapped into C0(R+).
DegreeMaster of Science (M.Sc.)
DepartmentMathematics and Statistics
SupervisorChoi, Yemon; Samei, Ebrahim
CommitteeAbou Salem, Walid; Bickis, Mik; Tanaka, Kaori
Copyright DateDecember 2013
Banach algebra, Module action, Compact and Weakly compact Derivations, T-set, TF-set.