The closure of the range of an elementary operator (Q1887508)
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scientific article; zbMATH DE number 2119140
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The closure of the range of an elementary operator |
scientific article; zbMATH DE number 2119140 |
Statements
The closure of the range of an elementary operator (English)
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26 November 2004
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For a Hilbert space \(H\), consider the operator \(\phi :B(H)\to B(H)\) defined by \(\phi (X)=AXB+CXD\), where \(A\), \(B\), \(C\), and \(D\) are some operators on \(H\). Certain conditions are given which are sufficient for \(B(H)\) to be the topological direct sum of \(\phi^{-1}(0)\) and the range of \(\phi\).
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elementary operator
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Hilbert space
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orthogonality
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isolated point of the spectrum
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hyponormal operator
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range closure
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