Characteristic conditions for a 𝑐₀-semigroup with continuity in the uniform operator topology for 𝑡>0 in Hilbert space

Abstract

In this paper, we obtain necessary and sufficient conditions for a c 0 {c_0} -semigroup with continuity in the uniform operator topology for t > 0 t > 0 in Hilbert space in terms of the spectral property of its infinitesimal generator. Then we get the characteristic theorem for the compact semigroup.