Perturbation of local \(C\)-semigroups
Let \(C\) be a bounded linear injective operator and \(A\) be the generator of a local \(C\)-semigroup \(\{S(t):0\leq t<T\}\) on a Banach space \(X\). It is proved that, if \(B\) is a bounded operator such that \(R(B)\subset R(C)\) and \(BCx=CBx\) for all \(x\in D(A)\), then \(A+B\) also generates a local \(C\)-semigroup.
scientific article; zbMATH DE number 5502881