Let 1 ≤ p < ∞ and (xn)nℕ be a sequence of positive elements in a non-commutative Lp space and (En)nℕ be an increasing sequence of conditional expectations, then ||∑n En(Xn|| ≤ cp ||∑n Xn||p. This inequality is due to Burkholder, Davis and Gundy in the commutative case. By duality, we obtain a version of Doob's maximal inequality for 1 < p ≤ ∞.
ASJC Scopus subject areas
- Applied Mathematics