On the extension of Hölder maps with values in spaces of continuous functions
| dc.creator | Lancien, Gilles | |
| dc.creator | Randrianantoanina, Beata | |
| dc.date | 2004-05-28 | |
| dc.date.accessioned | 2026-07-07T05:08:43Z | |
| dc.date.available | 2026-07-07T05:08:43Z | |
| dc.description | We study the isometric extension problem for Hölder maps from subsets of any Banach space into $c_0$ or into a space of continuous functions. For a Banach space $X$, we prove that any $α$-Hölder map, with $0<α\leq 1$, from a subset of $X$ into $c_0$ can be isometrically extended to $X$ if and only if $X$ is finite dimensional. For a finite dimensional normed space $X$ and for a compact metric space $K$, we prove that the set of $α$'s for which all $α$-Hölder maps from a subset of $X$ into $C(K)$ can be extended isometrically is either $(0,1]$ or $(0,1)$ and we give examples of both occurrences. We also prove that for any metric space $X$, the described above set of $\al$'s does not depend on $K$, but only on finiteness of $K$. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405565 | |
| dc.identifier | http://arxiv.org/abs/math/0405565 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71375 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20 (46T99, 54C20, 54E35) | |
| dc.title | On the extension of Hölder maps with values in spaces of continuous functions | |
| dc.type | text |