On the operator equation \(e^A=e^B\) (Q1864969)
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scientific article; zbMATH DE number 1886835
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the operator equation \(e^A=e^B\) |
scientific article; zbMATH DE number 1886835 |
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On the operator equation \(e^A=e^B\) (English)
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23 March 2003
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Let \(e^A= e^B\) for some Hilbert space operators \(A\) and \(B\). Suppose that \(A\) is normal with norm not exceeding \(\pi\). Then \(A^2 B= BA^2\). If the norm of \(A\) is strictly less than \(\pi\), then \(AB= BA\). Related or even stronger conclusions are obtained under additional (mostly spectral) conditions on \(A\) and \(B\).
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normal operators
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exponentials
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spectrum
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