Commutators of Hilbert-Schmidt operators. I
type: Item
instance of: scholarly article
title: Commutators of Hilbert-Schmidt operators. I
zbMATH Open document ID: 0618.47030
DOI: 10.1007/BF01202521
author: Gary Weiss
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: It is known that if D is a diagonal matrix with entries \(d,d_ 1,d_ 2,..\). where \(d_ n\downarrow 0\), \(\sum d_ n=d\), and if D is a finite sum of commutators of Hilbert-Schmidt operators, then \(\sum (\log n)d_ n<\infty\). In this paper the converse is proved providing a complete characterization of this class of Hilbert-Schmidt commutators and settling in the negative the related 1971 problem of Pearcy and Topping.
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 4002874
zbMATH Keywords: diagonal operators
zbMATH Keywords: weighted shifts
zbMATH Keywords: summable series
zbMATH Keywords: logarithmic behavior of matrices
zbMATH Keywords: finite sum of commutators of Hilbert-Schmidt operators
MaRDI profile type: Publication
cites work: Q3738112
cites work: Q5571194
cites work: On commutators in ideals of compact operators
cites work: Q3263053
cites work: Commutators of Hilbert-Schmidt operators II
description: scientific article; zbMATH DE number 4002874