On the best constants in noncommutative Khintchine-type inequalities
| dc.creator | Haagerup, Uffe | |
| dc.creator | Musat, Magdalena | |
| dc.date | 2006-11-07 | |
| dc.date | 2007-05-23 | |
| dc.date.accessioned | 2026-07-07T08:08:18Z | |
| dc.date.available | 2026-07-07T08:08:18Z | |
| dc.description | We obtain new proofs with improved constants of the Khintchine-type inequality with matrix coefficients in two cases. The first case is the Pisier and Lust-Piquard noncommutative Khintchine inequality for $p=1$, where we obtain the sharp lower bound of $\frac1{\sqrt{2}}$ in the complex Gaussian case and for the sequence of functions $\{e^{i2^nt}\}_{n=1}^\infty$ . The second case is Junge's recent Khintchine-type inequality for subspaces of the operator space $R\oplus C$, which he used to construct a cb-embedding of the operator Hilbert space $OH$ into the predual of a hyperfinite factor. Also in this case, we obtain a sharp lower bound of $\frac1{\sqrt{2}}$ . As a consequence, it follows that any subspace of a quotient of $(R\oplus C)^*$ is cb-isomorphic to a subspace of the predual of the hyperfinite factor of type $III_1$, with cb-isomorphism constant $\leq \sqrt{2}$ . In particular, the operator Hilbert space $OH$ has this property. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611160 | |
| dc.identifier | http://arxiv.org/abs/math/0611160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131222 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L51; 46L53; 47L25 | |
| dc.title | On the best constants in noncommutative Khintchine-type inequalities | |
| dc.type | text |