FACTORIZATION OF COMPLETELY BOUNDED BILINEAR OPERATORS AND INJECTIVITY

A completely bounded bilinear operator phi: MxM --> M on a von Neumann algebra. M is said to have a factorization in M if there exist comple tely bounded linear operators psi(j), theta(j): M --> M such that phi( x,y) = Sigma(j is an element of Lambda) psi(j)(x) theta(j)(y), x,y is an element of M where convergence of the sum is made precise below. Th e main result of the paper is that all completely bounded bilinear ope rators phi: MxM --> M have Factorizations in M if and only if,M is inj ective. (C) 1998 Academic Press.