TY - JOUR
T1 - Doob's inequality for non-commutative martingales
AU - Junge, Marius
PY - 2002
Y1 - 2002
N2 - 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 ≤ ∞.
AB - 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 ≤ ∞.
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U2 - 10.1515/crll.2002.061
DO - 10.1515/crll.2002.061
M3 - Article
AN - SCOPUS:0036339560
SN - 0075-4102
SP - 149
EP - 190
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 549
ER -