Embeddings of $\ell_p$ into non-commutative spaces
| dc.creator | Randrianantoanina, Narcisse | |
| dc.date | 2000-04-24 | |
| dc.date.accessioned | 2026-07-07T04:34:51Z | |
| dc.date.available | 2026-07-07T04:34:51Z | |
| dc.description | Let $\M$ be a semi-finite von Neumann algebra equipped with a faithful normal trace $τ$. We study the subspace structures of non-commutative Lorentz spaces $L_{p,q}(\M, τ)$, extending results of Carothers and Dilworth to the non-commutative settings. In particular, we show that, under natural conditions on indices, $\ell_p$ can not be embedded into $L_{p,q}(\M, τ)$. As applications, we prove that for $0<p<\infty$ with $p \neq 2$ then $\ell_p$ cannot be strongly embedded into $L_p(\M,τ)$. Thus providing a non-commutative extension of a result of Kalton for $0<p<1$ and a result of Rosenthal for $1\leq p <2$ on $L_p[0,1]$. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0004146 | |
| dc.identifier | http://arxiv.org/abs/math/0004146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59063 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L50; 47D15 | |
| dc.title | Embeddings of $\ell_p$ into non-commutative spaces | |
| dc.type | text |