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+).
| Identifer | oai:union.ndltd.org:USASK/oai:ecommons.usask.ca:10388/ETD-2013-12-1339 |
| Date | 2013 December 1900 |
| Contributors | Choi, Yemon, Samei, Ebrahim |
| Source Sets | University of Saskatchewan Library |
| Language | English |
| Detected Language | English |
| Type | text, thesis |
Page generated in 0.0023 seconds