Let X. Y be compact Hausdorff spaces, and E, F be Banach spaces. A linear map T¡GC (X¡AE)¡÷C (Y¡AF) is separating if ¡üTf(y)¡ü¡üTg(y)¡ü¡×0 whenever ¡üf(x)¡ü¡üg(x)¡ü¡×0, for every x belonging to X, y belonging to Y. Gau, Jeang and Wong prove that a biseparating linear bijection T is a weighted composition oprator Tf¡×hf¡³£p where h is a function from Y into the set of inveritable linear operators from E onto F and £p is a homeomorphism from Y onto X. In this thesis, we extend this result to the case that continuous functions are defined to a locally compact Hausdorff space, which is either £m-compact or first countable. Moreover, we give a short proof of a recent result of Mrcun. Finally, we give an alternative approach to an Araujo's result concerning biseparating maps of smooth functions appeared in Adv. Math.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0623105-210702 |
| Date | 23 June 2005 |
| Creators | Yan, Shao-hua |
| Contributors | Ngai-Ching Wong, Hwa-Long Gau, Mark C. Ho |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0623105-210702 |
| Rights | unrestricted, Copyright information available at source archive |
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