Doob's inequality for non-commutative martingales

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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 ≤ ∞.

Original languageEnglish (US)
Pages (from-to)149-190
Number of pages42
JournalJournal fur die Reine und Angewandte Mathematik
Issue number549
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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