Properties of C Semigroups
Wei Li · Journal of Chengdu University · 2011
New conditions of C semigroups are provided that(A1) there exists an angle θ∈(π/2,π] such that(1)ρ(A(t)){λ:|argλ|θ}∪{0} for each t∈;(2)there exists a positive constant M such that ‖R(λ,A(t))C‖≤M/|λ|,λ∈∑={λ:|argλ|θ}∪{0},t∈.(A2) For each λ∈∑,the operator valued function R(λ,A(t))C of t is continuously differentiable in in the uniform operator topology,and there exists positive constant K1 and ρ∈(0,1] such that ‖/tR(λ,A(t))C‖≤K1|λ|p,λ∈∑,t∈,under which the boundness of C semigroups is proved.