We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sqn in Sp (ℓq m) with optimal order m ∼ n2. Using these embeddings we show the surprising fact that the sharp type (cotype) index in the sense of operator spaces for Lp [0, 1] is min (p, p′) (max(p, p′)). Similar techniques are used to show that the operator space notions of B-convexity and K-convexity are equivalent.
- Noncommutative random variable
- Operator space
- Type and cotype
ASJC Scopus subject areas