An asymptotic Fuglede theorem for generators of \(C_ 0\) groups (Q1822031)
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scientific article; zbMATH DE number 4000820
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An asymptotic Fuglede theorem for generators of \(C_ 0\) groups |
scientific article; zbMATH DE number 4000820 |
Statements
An asymptotic Fuglede theorem for generators of \(C_ 0\) groups (English)
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1987
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Let \(e^{tA}\), \(e^{sB}(t,s\in R)\) be two commuting \(C_ 0\) groups of operators on the Banach space X with slow growth at infinity. In this case \(\| Ax-iBx\|\) can be made arbitrarily small when \(\| Ax+iBx\|\) is made small and \(\| x\| \leq 1\). This follows from an explicit inequality relating \(\| Ax-iBx\|\) and \(\| Ax+iBx\|\) for all \(x\in X\).
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commuting \(C_ 0\) groups of operators on the Banach space
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slow growth at infinity
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