ANALYT IC THEORY OF SUBNORMAL OPERATORS

Let S be a pure subnormal operator and #(.) be its mosaic introduced in [13]. In this paper, the author proves that rank t*(z) < +co if [S*, S] is compact and rank ~t(z) =-g(z) where g(.) 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. w This paper is a continuation of the author's previous paper [13]. In this paper, S is a pure subnormal operator on a separable Hilbert space)4 with minimal normal extension N on a separable HUbert space K D)4. The operator S ~ defined on)4 ' =