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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