Trace ideal criteria for Toeplitz operators
type: Item
instance of: scholarly article
title: Trace ideal criteria for Toeplitz operators
zbMATH Open document ID: 0618.47018
DOI: 10.1016/0022-1236(87)90072-3
author: Daniel H. Luecking
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: For a complex measure \(\mu\) on the open unit disk U define an operator \(T_{\mu}\) on a Hilbert space H of analytic functions with reproducing kernel k(z,w) by \(T_{\mu}f(w)=\int f(z)\overline{k(z,w)}d\mu (z)\). For a certain scale of Hilbert spaces \(H_{\alpha}\), \(\alpha <1\), which includes the Hardy space \(H^ 2\) and weighted Bergman spaces \(A^{2,\beta}\), conditions are obtained which imply \(T_{\mu}\) belongs to a Schatten ideal \({\mathcal S}_ p\). If \(\mu\) is a positive measure then these conditions are necessary and sufficient. Application to composition operators and restriction operators are indicated.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 46E20
zbMATH DE Number: 4002862
zbMATH Keywords: Hilbert space of analytic functions with reproducing kernel
zbMATH Keywords: scale of Hilbert spaces
zbMATH Keywords: Hardy space
zbMATH Keywords: weighted Bergman spaces
zbMATH Keywords: Schatten ideal
zbMATH Keywords: composition operators
zbMATH Keywords: restriction operators
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90072-3
OpenAlex ID: W2090353347
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description: scientific article; zbMATH DE number 4002862