Some Properties of Eventually Norm Continuous Semigroups
Lianping Zhang · Journal of Shanxi University · 2005
Some properties of eventually norm-continuous semigroups｛T(t)｜t≥0｝ in Banach space for tt_0(t_0≥0) was studied,and a spectral distribution properies for infinitesimal generators of eventually norm-continuous semigroups was got.The main theorm was as follows.Let T(t) be a C_0-semigroup with its generator A on a Banach space X,ω_0=(inf)t0(1tln‖T(t)‖).Suppose T(t) was eventually norm-continuous for tα≥0,then there exited a decreasing function φ:(0,∞)→R such that φ(M)→∞(M→∞) and S=｛λ∈C｜Reλ≥φ(｜Imλ｜)｝ρ(A),ρ(A) stands for resolvent set of A.