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Compact and weakly compact Derivations on l^1(Z_+)

Date

2013-12-24

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Degree Level

Masters

Abstract

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 [6], 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+).

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Keywords

Banach algebra, Module action, Compact and Weakly compact Derivations, T-set, TF-set.

Citation

Degree

Master of Science (M.Sc.)

Department

Mathematics and Statistics

Program

Mathematics

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