Let X be a compact metric space, and Lip(X) is the space of all bounded real-valued Lipschitz functions on X. A linear map T:Lip(X)->Lip(Y) is called disjointness preserving if fg=0 in Lip(X) implies TfTg=0 in Lip(Y). We prove that a biseparating linear bijection T(i.e. T and T^-1 are separating) is a weighted composition operator Tf=hf¡³£p, f is Lipschitz space from X onto R, £p is a homeomorphism from Y onto X, and h(y) is a Lipschitz function in Y.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0903107-134219 |
| Date | 03 September 2007 |
| Creators | Wu, Tsung-che |
| Contributors | none, none, none, none |
| 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-0903107-134219 |
| Rights | unrestricted, Copyright information available at source archive |
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