THE REDUCTION PROPERTY AND COMPLETE UNITARY INVARIANT OF A CLASS OF OPERATORS

M. J. Cowen and R. G. Douglas studied operators in B_n(Ω) from the point of view of complex geometry (Acta Math., 141(1978), 187—261). They got some unitary invariants of operators in B_n(Ω) using the curvature of the vector bundle related to the operator. Especially, when n=1, the curvature itself is a complete unitary