The analytic model of a hyponormal operator with rank one self-commutator
type: Item
instance of: scholarly article
title: The analytic model of a hyponormal operator with rank one self-commutator
zbMATH Open document ID: 0592.47013
DOI: 10.1007/BF01238864
author: Joel D. Pincus
author: Jingbo Xia
author: Daoxing Xiao
published in: Integral Equations and Operator Theory
publication date: 1984-01-01T00:00:00Z
review text: 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 \(H^ 2(D)\).
reviewed by: Katsutoshi Takahashi
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 3951349
zbMATH Keywords: analytic model
zbMATH Keywords: completely hyponormal operator with rank one self- commutator
zbMATH Keywords: principal function
zbMATH Keywords: Cauchy integral representation
zbMATH Keywords: adjoint of the model operator
zbMATH Keywords: eigenvectors
zbMATH Keywords: Hardy space
MaRDI profile type: Publication
cites work: An Invariant for Certain Operator Algebras
cites work: Mosaics, principal functions, and mean motion in von Neumann algebras
cites work: Principal functions, index theory, geometric measure theory and function algebras
cites work: Q3812793
cites work: An integrality theorem for subnormal operators
cites work: Complex geometry and operator theory
cites work: Q5565773
cites work: The Gauss-Green Theorem
cites work: Analytic capacity and measure
cites work: Symmetric and self-adjoint Toeplitz operators on multiply connected plane domains
cites work: On the analytic model of a class of hyponormal operators
cites work: On the kernels associated with a class of hyponormal operators
cites work: Spectral theory of hyponormal operators
description: scientific article; zbMATH DE number 3951349