Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\) (Q1208270)
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scientific article; zbMATH DE number 166222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\) |
scientific article; zbMATH DE number 166222 |
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Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\) (English)
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16 May 1993
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The authors consider the equation \(T(H^{1/n} T)^ n=K\) with some natural number \(n\) and \(H\), \(K\) being positive operators on a Hilbert space (\(H\) is nonsingular). The purpose of the paper is to show that the existence of the solution \(T\) to this equation for some number \(m>0\) need not provide the solvability of the equation for any natural \(n<m\). The results continue previous investigations of the authors.
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operator equation
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positive operators on a Hilbert space
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