Suppose that X is a right process which is associated with a semi-Dirichlet form (ε, D(ε)) on L2(E; m). Let J be the jumping measure of (ε, D(ε)) satisfying J(E x E- d) 〈 ∞. Let u E D(ε)b := D(ε) N L(E; m), we have the following Pukushima's decomposition u(Xt)-u(X0) --- Mut + Nut. Define Pu f(x) = Ex[eNT f(Xt)]. Let Qu(f,g) = ε(f,g)+ε(u, fg) for f, g E D(ε)b. In the first part, under some assumptions we show that (Qu, D(ε)b) is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then (Put〉0is strongly continuous on L2(E;m). If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J(E x E - d) 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf(x) = Ex[eAtf(Xt)] to be strongly continuous.