On The Property And Applications Of The Yosida Approximation

In this paper, three full characterizations and a sufficient condition are given, in terms of the Yosida Approximation of the infinitesimal generator A of a C0 semigroup T(t) on a Banach space X, which assure respectively the differentiability of T(t) for t ≥ t0(t0 ≥ 0), the continuity of T(t) for t ≥ t0(t0 ≥ 0) in the uniform operator topology and the differentiability of T(t) for t > t0(t0 ≥ 0).