Notes on Matrix Valued Paraproducts
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چکیده
X iv :m at h/ 05 12 40 7v 2 [ m at h. FA ] 1 8 Ja n 20 06 Notes on Matrix Valued Paraproducts Tao MEI 1 Abstract Denote by Mn the algebra of n×n matrices. We consider the dyadic paraproducts πb associated with Mn valued functions b, and show that the L(Mn) norm of b does not dominate ||πb||L2(l2n)→L2(l2n) uniformly over n. We also consider paraproducts associated with noncommutative martingales and prove that their boundedness on bounded noncommutative Lp−martingale spaces implies their boundedness on bounded noncommutative Lq−martingale spaces for all 1 < p < q < ∞.
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