TY - JOUR
T1 - Maximal theorems of Menchoff-Rademacher type in non-commutative Lq-spaces
AU - Defant, Andreas
AU - Junge, Marius
N1 - ·Corresponding author. E-mail addresses: [email protected] (A. Defant), [email protected] (M. Junge). 1Marius Junge is partially supported by the NSF.
PY - 2004/1/15
Y1 - 2004/1/15
N2 - 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.
AB - 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.
KW - Maximal function
KW - Non-communitative L-spaces
KW - Unconditional sequences
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U2 - 10.1016/j.jfa.2002.07.001
DO - 10.1016/j.jfa.2002.07.001
M3 - Article
AN - SCOPUS:0346499342
SN - 0022-1236
VL - 206
SP - 322
EP - 355
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -