Commutators of Hilbert-Schmidt operators. I (Q1822329)
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scientific article; zbMATH DE number 4002874
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Commutators of Hilbert-Schmidt operators. I |
scientific article; zbMATH DE number 4002874 |
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Commutators of Hilbert-Schmidt operators. I (English)
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1986
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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.
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diagonal operators
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weighted shifts
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summable series
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logarithmic behavior of matrices
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finite sum of commutators of Hilbert-Schmidt operators
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