【摘要】 主要给出了一个在Hilbert空间中最终范数连续半群的扰动定理.设T(t)为Hilbert空间H上的C0半群,当t>t0≥0时按范数连续,A为其无穷小生成元.又设B是A相对有界的,D(A)D(B),T(t)B BT(t),且存在δ>0使得K0<+∞.这里Kλ=sup∫0δe-λt‖BT(t)x‖dt x∈D(A),‖x‖≤1,(λ≥0).则当2ε<1/limKλ时,A+εB生成半群TB(t)且TB(t)当t>2t0时按范数连续.更多还原

【Abstract】 A was obtained new perturbation theorem for eventually norm-continuous semigroups on a Hilbert space.Let the linear operator A is an infinitesimal generator of a C₀ semigroup T（t） which is norm-continuous for t>t₀≥0 in Hilbert space H.And let B be a linear operator from D（A）（domain of A） to D（B） satisfying T（t）BBT（t） and there exists δ>0 such that K₀<+∞ where K_λ=sup∫^δ₀e^-λt‖BT（t）x‖dt｜x∈D（A）,‖x‖≤1,when 2｜ε｜<1/（lim）λ→+∞K_λ,semigroup T_B（t） generated by A+εB is norm-continuous for t>2t₀.更多还原