THE BERGER-SHAW THEOREM FOR CYCLIC SUBNORMAL-OPERATORS

This work gives a sharp form of the Berger-Shaw Theorem for cyclic sub normal operators. That is, if S is a cyclic subnormal operator, then S has trace class self-commutator and the trace equals (1/pi)Area[sigma (S) - sigma(e)(S)]. It also characterizes those functions f such that S(S) has trace class self-commutator and computes the trace as the Dir ichlet integral of (f) over cap on the set of analytic bounded point e valuations for S. The technique used also gives some partial results f or rationally cyclic subnormal operators.