On the condition of operator-valued moment problem (Q1334082)

In this short notice the author discusses necessary and sufficient conditions for the expression of a sequence of operators on a Hilbert space through moments of some operator-valued function with compact support. Using the theory of subnormal operators the key theorem is proved. It is shown that the sequence of operators mentioned above to satisfy the moment equation may satisfy another operator equation that involves an exponent function of operator series being represented through another series with (power series) coefficients as the sequence of positive operators.