Perturbations and Approximations
Let X be a Banach space and let A be the infinitesimal generator of a C 0 semigroup T(t) on X, satisfying || T(t)|| ≤ Me wt . If B is a bounded linear operator on X then A + B is the infinitesimal generator of a C0semigroup S(t) on X, satisfying ||S(t)|| ≤ Me(w + M || B ||)t.
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