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On the left multiplicative perturbations of \(C\)-regularized resolvent families. (Chinese. English summary) Zbl 1174.47345
Summary: The multiplicative perturbations of \(C\)-regularized resolvent families defined in a Banach space \(X\) are studied. By using the approach of basic operator theory, a left multiplicative perturbation theorem of \(C\)-regularized resolvent families is proved.

MSC:
47D60 \(C\)-semigroups, regularized semigroups
47A55 Perturbation theory of linear operators
47D09 Operator sine and cosine functions and higher-order Cauchy problems
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