Operator Khintchine inequality in non-commutative probability (Q5927630)

The classical Khinchine inequality shows that in the class of linear combinations of Rademacher functions all the \(L_p\) norms, for \(2\leq p<\infty\), are equivalent. The far reaching generalization presented in the paper consists of replacing the scalar coefficients by operators from the corresponding Schatten classes, and the Rademacher functions by a family of non-commuting random variables. Several examples of such families are given. In many cases, one gets optimal constants in the non-commutative Khinchine inequality.