The analytic model of a hyponormal operator with rank one self-commutator
Let H be a completely hyponormal operator with rank one self-commutator. The authors prove that H is unitarily equivalent to the operator \(M_ z\) of multiplication by z, \((M_ zf)(z)=zf(z)\), on a Hilbert space of functions on the spectrum of H with inner product described in terms of the principal function of H. Then they give a Cauchy integral representation for the adjoint of the model operator and consider its eigenvectors. Their model is applied to prove that if the principal function of H is the characteristic function of a multiply connected domain D whose boundary consists of a finite number of analytic contours, then H is similar to \(M_ z\) on the Hardy space \(H^ 2(D)\).
completely hyponormal operator with rank one self- commutator
scientific article; zbMATH DE number 3951349