J rgens结果的一个新证明

A New Proof of Jorgens′s Result

文章研究有界线性算子半群的扰动问题 .在一定条件下 ,我们表明 :设算子 B生成最终依范连续半群 S(t) (t τ) ,K是有界线性算子 .如果‖ K R(σ+iτ,B) K‖→ 0 ,τ→∞ ,那么算子 A =B +K生成的半群 T(t) ,t>2τ是依范连续的 .我们将此结果应用于迁移算子 ,给出 J rgens结果的一个新证明 .

The perturbation problem of bounded linear operator semigroup is studied in the present paper. Under some conditions we show that if B generates the semigroup S(t) that is continuous in the sense of norm for tτ, and K is bounded linear operator satisfying‖KR(σ+iτ, B)K‖→0, τ→∞then the semigroup generated by A=B+K also is continuous in the sense of norm for t2τ. We apply this result to transport and give a new proof of Jorgens′s result.