1-complemented subspaces of spaces with 1-unconditional bases
| dc.creator | Randrianantoanina, Beata | |
| dc.date | 1996-05-09 | |
| dc.date.accessioned | 2026-07-07T09:15:31Z | |
| dc.date.available | 2026-07-07T09:15:31Z | |
| dc.description | We prove that if $X$ is a complex strictly monotone sequence space with $1$-unconditional basis, $Y \subseteq X$ has no bands isometric to $\ell_2^2$ and $Y$ is the range of norm-one projection from $X$, then $Y$ is a closed linear span a family of mutually disjoint vectors in $X$. We completely characterize $1$-complemented subspaces and norm-one projections in complex spaces $\ell_p(\ell_q)$ for $1 \leq p, q < \infty$. Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are $1$-complemented in (real or complex) Orlicz or Lorentz sequence spaces. In particular if an Orlicz or Lorentz space $X$ is not isomorphic to $\ell_p$ for some $1 \leq p < \infty$ then the only subspaces of $X$ which are $1$-complemented and disjointly supported are the closed linear spans of block bases with constant coefficients. | |
| dc.identifier | https://arxiv.org/abs/math/9605214 | |
| dc.identifier | http://arxiv.org/abs/math/9605214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153045 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20, 46B45, 41A65 | |
| dc.title | 1-complemented subspaces of spaces with 1-unconditional bases | |
| dc.type | text |