Daoxing Xia

Analytic theory of subnormal operators

LetS be a pure subnormal operator and μ(·) be its mosaic introduced in [13]. In this paper, the author proves that rank μ(z)<+∞ if [S*,S] is compact and rank μ(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.

The analytic model of a subnormal operator

The analytic model of a pure subnormal opertor and its conjugate subnormal operator is obtained. A mosaic is introduced for subnormal operator. Some results in spectral analysis of subnormal operators are obtained by means of the analytic model and the mosaic. The form of pure subnormal operators with rank two self-commutator is determined.

ON PURE SUBNORMAL OPERATORS WITH FINITE RANK SELF-COMMUTATORS AND RELATED OPERATOR, TUPLES

In this paper, we study the model of a pure subnormal operator with finite rank self-commutator and of the relatedn-tuple of commuting linear bounded operators. We also give some applications of the model to the theory ofn-tuples of commuting operators with trace class self-commutators.

Trace formulas for almost commuting operators, cyclic cohomology and subnormal operators

Some formulas related to cyclic cohomology for the trace of the product of commutators are established. A simple complete unitary invariant for some subnormal operator with simply connected spectrum is found.

Compact products of Hankel operators

AbstractIn this paper we completely characterize compact products of three Hankel operators on the Hardy space. We obtain a necessary and sufficient condition for that

COMPLETE UNITARY INVARIANT :FOR SOME SUBNORMAL OPERATOR

H_{f_1 }^* H_{f_2 } H_{f_3 }^* ,H_{f_2 }^* H_{f_1 } H_{f_3 }^*

On a class of operators with finiterank self-commutators

, and