Interpolation between non-commutative BMO and non-commutative Lp-spaces

We prove that for 1 less than or equal to p < q < infinity the analogue of the classical result [BMO, L-p](p/q) = L-q holds in the setting of a finite von Neumann algebra M, equipped with an increasing filtration (M-n)(ngreater than or equal to1) of von Neumann subalgebras. We also obtain the corresponding results for the real method of interpolation. We discuss the appropriate operator space matrix norms and show that these interpolation results hold in the category of operator spaces. (C) 2003 Elsevier Science (USA). All rights reserved.