The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators
| dc.creator | Lust-Piquard, Françoise | |
| dc.creator | Xu, Quanhua | |
| dc.date | 2006-09-13 | |
| dc.date.accessioned | 2026-07-07T07:24:47Z | |
| dc.date.available | 2026-07-07T07:24:47Z | |
| dc.description | We prove the little Grothendieck theorem for any 2-convex noncommutative symmetric space. Let $\M$ be a von Neumann algebra equipped with a normal faithful semifinite trace $\t$, and let $E$ be an r.i. space on $(0, \8)$. Let $E(\M)$ be the associated symmetric space of measurable operators. Then to any bounded linear map $T$ from $E(\M)$ into a Hilbert space $\mathcal H$ corresponds a positive norm one functional $f\in E_{(2)}(\M)^*$ such that $$\forall x\in E(\M)\quad \|T(x)\|^2\le K^2 \|T\|^2 f(x^*x+xx^*),$$ where $E_{(2)}$ denotes the 2-concavification of $E$ and $K$ is a universal constant. As a consequence we obtain the noncommutative Khintchine inequalities for $E(\M)$ when $E$ is either 2-concave or 2-convex and $q$-concave for some $q<\8$. We apply these results to the study of Schur multipliers from a 2-convex unitary ideal into a 2-concave one. | |
| dc.description | 14 pages. To appear in J. Funct. Anal | |
| dc.identifier | https://arxiv.org/abs/math/0609356 | |
| dc.identifier | http://arxiv.org/abs/math/0609356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116497 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 46L52; Secondary 46L50; 47A63 | |
| dc.title | The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators | |
| dc.type | text |