Abstract
Estimates for maximal functions provide the fundamental tool for solving problems on pointwise convergence. This applies in particular for the Menchoff–Rademacher theorem on orthogonal series in L 2[0,1] and for results due independently to Bennett and Maurey–Nahoum on unconditionally convergent series in L 1[0,1]. We prove corresponding maximal inequalities in non-commutative L q -spaces over a semifinite von Neumann algebra. The appropriate formulation for non-commutative maximal functions originates in Pisier's recent work on non-commutative vector valued L q -spaces.
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