Similarity of multiplication operators on the Sobolev disk algebra
type: Item
instance of: scholarly article
title: Similarity of multiplication operators on the Sobolev disk algebra
zbMATH Open document ID: 1279.47051
author: Kui Ji
author: Rui Shi
publication date: 2013-03-28T00:00:00Z
review text: Let \(\mathbb{D}\) be the unit disk. Introduce the Sobolev space \(W^{22}(\mathbb{D})\), which consists of all functions \(f \in L^2(\mathbb{D})\) whose distributional partial derivatives of the first and second orders belong to \(f \in L^2(\mathbb{D})\) and its subspace \(R(\mathbb{D})\), which is generated by the rational functions with poles outside \(\mathbb{D}\). The main result of the paper states that, given two functions \(f\) and \(g\) being analytic on the closure of the unit disk, the multiplication operator \(M_f\) is similar to \(M_g\) if and only if there exist two finite Blaschke products \(B\) and \(B_1\) of the same order and a function \(h\) analytic on \(\mathbb{D}\) such that \(f = h \circ B\) and \(g = h \circ B_1\).
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B32
Mathematics Subject Classification ID: 19K14
zbMATH DE Number: 6149096
zbMATH Keywords: Sobolev space
zbMATH Keywords: Sobolev disk algebra
zbMATH Keywords: multiplication operator
zbMATH Keywords: similarity
MaRDI profile type: Publication
full work available at URL: s10114-013-1745-8
OpenAlex ID: W1968916514
cites work: Finite Blaschke product and the multiplication operators on Sobolev disk algebra
cites work: Similarity Classification of Cowen-Douglas Operators
cites work: K-group and similarity classification of operators
cites work: Similarity classification of holomorphic curves
cites work: The commutant and similarity invariant of analytic Toeplitz operators on Bergman space
cites work: Similarity of analytic Toeplitz operators on the Bergman spaces
cites work: Forward and Reverse Carleson Inequalities for Functions in Bergman Spaces and Their Derivatives
cites work: Complex geometry and operator theory
cites work: Q4422023
DOI: 10.1007/S10114-013-1745-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6149096