On pure subnormal operators with finite rank self-commutators and related operator tuples

On a Class of Operators of Finite Type

“…[4]) of S, then σ(N ) = L S ∪ Q, where Q is a finite set. The measure e(·) defined in (30) coincides with the measure e(·) defined in [14] and [16] on σ(N ) \ Q, (see also the begining of §5 of the present paper. ).…”

“…Let us briefly quote some in [16] and [19]. Let D be a finitely connected domain with boundary ∂D consisting of finite collection of piecewise smooth Jordan curves in a Riemann surface R. If there are a bounded analytic function Ψ(·) and a meromorphic function S(·) on D which have continuous boundary values on ∂D satisfying…”

Right Spectrum and Trace Formula of Subnormal Tuples of Operators of Finite Type

“…Actually theseŜ j (·) are branches of multivalued Schwarz functions associated with those subnormal operators S j (cf. [1,19,20,21]), j = 1, 2, . .…”

“…(minimal normal extension), i. e. there is no improper reducing subspace of N in K H. S is said to be pure, if there is no improper reducing subspace of S in H. Yakubovich [23,24] called a subnormal operator with finite rank self-commutator as a subnormal operator of finite type, cf. also [19,20,22]. Let us call a subnormal k-tuple of operators S = (S 1 , .…”

“…In this paper we only study pure subnormal k-tuple of operators S of finite type on H. Xia IEOT The main mathematical tool of this study is the analytic model of S in [15,16,17,19]. Let…”