| Full text | |
| Author(s): |
Candido, Leandro
Total Authors: 1
|
| Document type: | Journal article |
| Source: | STUDIA MATHEMATICA; v. 232, n. 1, p. 1-6, 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
For a locally compact Hausdorff space K and a Banach space X let C-0(K, X) denote the space of all continuous functions f : K -> X which vanish at infinity, equipped with the supremum norm. If X is the scalar field, we denote C-0(K, X) simply by C-0(K). We prove that for locally compact Hausdorff spaces K and L and for a Banach space X containing no copy of c(0), if there is an isomorphic embedding of C-0(K) into C-0(L, X), then either K is finite or vertical bar K vertical bar <= vertical bar L vertical bar. As a consequence, if there is an isomorphic embedding of C-0(K) into C-0(L, X) where X contains no copy of c(0) and L is scattered, then K must be scattered. (AU) | |
| FAPESP's process: | 12/15957-6 - On Banach spaces $C_0 (K, X)$ and the topology of $K$. |
| Grantee: | Leandro Candido Batista |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |