Second derivatives of norms and contractive complementation in vector-valued spaces
| dc.creator | Lemmens, Bas | |
| dc.creator | Randrianantoanina, Beata | |
| dc.creator | van Gaans, Onno | |
| dc.date | 2005-11-02 | |
| dc.date.accessioned | 2026-07-07T06:50:39Z | |
| dc.date.available | 2026-07-07T06:50:39Z | |
| dc.description | We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces $\ell_p(X)$, where $X$ is a Banach space with a 1-unconditional basis and $p \in (1,2)\cup (2,\infty)$. If the norm of $X$ is twice continuously differentiable and satisfies certain conditions connecting the norm and the notion of disjointness with respect to the basis, then we prove that every 1-complemented subspace of $\ell_p(X)$ admits a basis of mutually disjoint elements. Moreover, we show that every contractive projection is then an averaging operator. We apply our results to the space $\ell_p(\ell_q)$ with $p,q\in (1,2)\cup (2,\infty)$ and obtain a complete characterization of its 1-complemented subspaces. | |
| dc.description | 22 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0511044 | |
| dc.identifier | http://arxiv.org/abs/math/0511044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104732 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B45, 46B04 (Primary) 47B37 (Secondary) | |
| dc.title | Second derivatives of norms and contractive complementation in vector-valued spaces | |
| dc.type | text |