On a class of operators with finite rank self-commutators
This paper studies the class of pure operators \(A\) on a Hilbert space \(H\) satisfying \(\dim K_A< \infty\), where \(K_A= \bigvee^\infty_{n= 0} A^{*n}[A^*, A]H\). The main tool is a pair of matrices \(C_A= [A^*, A]|K_A\), and \(\Lambda_A= (A^*|K_A)^*\). A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class.
scientific article; zbMATH DE number 1310387