On the best constants in noncommutative Khintchine-type inequalities
On the best constants in noncommutative Khintchine-type inequalities
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关于非交换辛钦型不等式中的最佳常数
DOI：
10.1016/j.jfa.2007.05.014
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发表时间：
2006
影响因子：
1.7
通讯作者：
Magdalena Musat
中科院分区：
文献类型：
--
作者：
U. Haagerup;Magdalena Musat
在两种情况下，我们得到了带矩阵系数的Khintchine型不等式的改进常数的新证明。第一种情形是p=1的Pisier和Lust-Piquard非对易Khintchine不等式，其中我们得到了复高斯情形和函数序列的12的精确下界[公式：见正文]。第二种情况是Junge最近关于算子空间R⊕C的子空间的Khintchine型不等式，他用它构造了算子Hilbert空间OH到超有限因子的预对偶的CB嵌入.在这种情况下，我们还得到了一个精确的下界12。由此，(R⊕C)∗的商的任意子空间都CB同构于III1型超有限因子的预对偶子空间，且Cb同构常数⩽2。特别地，算子Hilbert空间OH具有这一性质。
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 12 in the complex Gaussian case and for the sequence of functions [Formula: see text] . The second case is Junge's recent Khintchine-type inequality for subspaces of the operator space R⊕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 12. As a consequence, it follows that any subspace of a quotient of (R⊕C)∗is cb-isomorphic to a subspace of the predual of the hyperfinite factor of type III1, with cb-isomorphism constant⩽2. In particular, the operator Hilbert space OH has this property.