An extrapolation of operator-valued dyadic paraproducts

We consider the dyadic paraproducts pi(phi) on T associated with an M-valued function phi. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L-p(T, L-p(M)) for some 1 < p < infinity implies their boundedness on L-p(T, L-p(M)) for all 1 < p < infinity provided that phi is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on L-p(T, L-p(M)).