Sequences in non-commutative L^p-spaces
| dc.creator | Randrianantoanina, Narcisse | |
| dc.date | 2000-04-24 | |
| dc.date.accessioned | 2026-07-07T04:34:50Z | |
| dc.date.available | 2026-07-07T04:34:50Z | |
| dc.description | Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $τ$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant quasi-Banach function space $E$ on the positive semi-axis is $α$-convex with constant 1 and satisfies a non-trivial lower $q$-estimate with constant 1, then the corresponding non-commutative space of measurable operators $E({\cal M}, τ)$ has the following property: every bounded sequence in $E({\cal M}, τ)$ has a subsequence that splits into a $E$-equi-integrable sequence and a sequence with pairwise disjoint projection supports. This result extends the well known Kadec-Pełczyński subsequence decomposition for Banach lattices to non-commutative spaces. As applications, we prove that for $1\leq p <\infty$, every subspace of $L^p(\cal M, τ)$ either contains almost isometric copies of $\ell^p$ or is strongly embedded in $L^p(\cal M, τ)$. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0004144 | |
| dc.identifier | http://arxiv.org/abs/math/0004144 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59061 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L50,47D15 | |
| dc.title | Sequences in non-commutative L^p-spaces | |
| dc.type | text |