Trace formulas for a class of subnormal tuples of operators

Trace formulas are established for the product of commutators related to subnormal tuple of operators (S₁,...,S_n) with minimal normal extension (N₁,...,N_n) satisfying conditions that sp(S_j)/sp(N_j) is simply-connected with smooth boundary Jordan curve sp(N_i) and [S_j^*,S_j]^1/2 L¹,j=1, 2,...,n.Some complete unitary invariants related to the trace formulas are found.This work is supported in part by NSF Grant no. DMS-9101268.