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 L2[0, 1] and for results due independently to Bennett and Maurey-Nahoum on unconditionally convergent series in L1 [0, 1]. We prove corresponding maximal inequalities in non-commutative Lq-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 Lq-spaces.
Original language | English (US) |
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Pages (from-to) | 322-355 |
Number of pages | 34 |
Journal | Journal of Functional Analysis |
Volume | 206 |
Issue number | 2 |
DOIs | |
State | Published - Jan 15 2004 |
Keywords
- Maximal function
- Non-communitative L-spaces
- Unconditional sequences
ASJC Scopus subject areas
- Analysis