Hankel and Toeplitz transforms on \(H^1\): continuity, compactness and Fredholm properties
type: Item
instance of: scholarly article
title: Hankel and Toeplitz transforms on \(H^1\): continuity, compactness and Fredholm properties
zbMATH Open document ID: 1201.47032
published in: Integral Equations and Operator Theory
publication date: 2009-10-19T00:00:00Z
review text: The paper is devoted to the study of continuity, compactness and Fredholm properties of Hankel operators \(H_\varphi\) and Toeplitz operators \(T_\varphi\) on the Hardy space \(H^1(\mathbb{T})\), where \(\mathbb{T}\) denotes the unit circle in the complex plane. A new proof for the characterization of the boundedness of \(H_\varphi\) (by means of the symbol \(\varphi\)) is provided. Additionally, the authors obtain a precise estimate for the operator norm of \(H_\varphi : H^1(\mathbb{T}) \rightarrow H^1(\mathbb{T})\) and a characterization of the compactness of \(H_\varphi \) on \(H^1(\mathbb{T})\). The Fredholm property of \(T_\varphi\) on \(H^1(\mathbb{T})\) is characterized in the case of not necessarily continuous functions \(\varphi\), and a formula for the corresponding Fredholm index of \(T_\varphi\) is also derived.
reviewed by: L. P. Castro
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 30H10
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 5617558
zbMATH Keywords: Hankel operator
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: compactness
zbMATH Keywords: boundedness
zbMATH Keywords: bounded mean oscillation
zbMATH Keywords: Fredholmness
author: Michael Papadimitrakis
author: J. A. Virtanen
MaRDI profile type: Publication
full work available at URL: s00020-008-1609-2
OpenAlex ID: W2017473189
DOI: 10.1007/S00020-008-1609-2
description: scientific article; zbMATH DE number 5617558