Maximal theorems of Menchoff-Rademacher type in non-commutative Lq-spaces |
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Authors: | Andreas Defant |
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Affiliation: | a Fachbereich Mathematik, Carl von Ossietzky Universität, Postfach 2503, D-26111 Oldenburg, Germany b Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall MC 382, 1409 West Green Street, Urbana, IL 61801, USA |
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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. |
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Keywords: | Maximal function Unconditional seqeunces Non-commutative Lq-spaces |
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