The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems (Q803909)
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scientific article; zbMATH DE number 4198875
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems |
scientific article; zbMATH DE number 4198875 |
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The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems (English)
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1992
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Conditions are considered under which the operator equation \(AX-XB=C\), where A and -B are generators of \(C_ 0\)-semigroups in Banach spaces, has a bounded solution. The results are then applied to obtain various conditions under which the solution of the abstract Cauchy problem \(dx/dt=Ax(t)+f(t),\) \(t\geq 0\), \(x(0)=x_ 0\), is asymptotically almost periodic.
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Bohr spectrum
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asymptotically almost periodic solution
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operator equation
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generators of \(C_ 0\)-semigroups in Banach spaces
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abstract Cauchy problem
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