Abstract. Given a vector space of Hilbert space valued integrable functions $H$, it is of interest to know whether every scalar integrable function can be written as a pointwise scalar product of functions in $H$. We give a result of this type in which the assumptions on $H$ are rather weak. In particular, we weaken the requirement on the existence of weakly null `special' sequences in $H$. We show how the abstract factorization result can be applied to the study of certain algebras related with subnormality.

AMS Subject Classification (1991): 47D25, 47B20

Received August 12, 1996 and in revised form February 25, 1997. (Registered under 5789/2009.)