论文标题
双连续半群的Lumer-Phillips类型生成定理
A Lumer-Phillips type generation theorem for bi-continuous semigroups
论文作者
论文摘要
著名的1960年代的Lumer-Phillips定理指出，Banach Space $ x $上的封闭且定义的操作员$ a \ colon d（a）\ subseteq x \ rightarrow x $ x $在$（a，d（a））$ avisipative and $ $ formip $ formip ys $ formetive $ formipive $（A，d（a）时，才会产生强烈的连续收缩半元素。在本文中，我们为双连续半群建立了此结果的版本，并将后者在其他示例中应用于传输方程，以及在无限网络上流动。
The famous 1960s Lumer-Phillips Theorem states that a closed and densely defined operator $A\colon D(A)\subseteq X\rightarrow X$ on a Banach space $X$ generates a strongly continuous contraction semigroup if and only if $(A,D(A))$ is dissipative and the range of $λ-A$ is surjective in $X$ for some $λ>0$. In this paper, we establish a version of this result for bi-continuous semigroups and apply the latter amongst other examples to the transport equation as well as to flows on infinite networks.
