Analytic theory of subnormal operators

LetS be a pure subnormal operator and (·) be its mosaic introduced in 13]. In this paper, the author proves that rank (z)<+ if S ^*,S] is compact and rank (z)=–g(z) whereg(·) is the Pincus principal function if S ^*,S] is in the trace class. Also a result is given about the form of pure and irreducible subnormal operators with finite rank self-commutators.This work is supported in part by a NSF grant.