Derivations decreasing the spectral radius (Q689652)
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scientific article; zbMATH DE number 446280
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Derivations decreasing the spectral radius |
scientific article; zbMATH DE number 446280 |
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Derivations decreasing the spectral radius (English)
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15 November 1993
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The following theorem is proved: Let \(A\) be a unital Banach algebra and let \(d\) be an inner derivation of \(A\). Suppose that for some positive number \(M\) and for all \(x\in A\) the inequality \(r(d(x))\leq Mr(x)\) holds. Then \(d\) maps \(A\) into \(\text{rad}(A)\).
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unital Banach algebra
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inner derivation
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