FACTORIZATION THROUGH HILBERT-SPACE AND THE DILATION OF L(X,Y)-VALUEDMEASURES

We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X, Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condit ion we derive the main results of Rosenberg, Makagon and Salehi, and M iamee without the assumption that X and/or Y are Hilbert spaces. In ad dition we relate the dilation problem to the problem of factoring a fa mily of operators through a single Hilbert space.