论文标题
最终阳性操作员半群的光谱和收敛性
Spectrum and convergence of eventually positive operator semigroups
论文作者
论文摘要
正面$ C_0 $ -Semigroups在功能空间（或在Banach Lattices上）的一个有趣的功能是，它们的长期行为比对一般半群的描述要容易得多。特别是，由于时间倾向于无穷大的时间，半群操作员（强烈或在操作员规范中）的收敛性可以由一组简单的光谱和紧凑条件来表征。 在本文中，我们表明，对于较大的（均匀）最终的阳性半群，类似的定理仍然是正确的 - 最近在研究各种混凝土微分方程的研究中出现了类似的定理。 我们的特征之一的主要一步是展示著名的Niiro-Sawashima定理的版本，最终是正面运营商的。积极的运营商和半群的几个证明在我们的环境中不再起作用，需要不同的论点，并给我们的方法带来了独特的风味。
An intriguing feature of positive $C_0$-semigroups on function spaces (or more generally on Banach lattices) is that their long-time behaviour is much easier to describe than it is for general semigroups. In particular, the convergence of semigroup operators (strongly or in the operator norm) as time tends to infinity can be characterized by a set of simple spectral and compactness conditions. In the present paper, we show that similar theorems remain true for the larger class of (uniformly) eventually positive semigroups - which recently arose in the study of various concrete differential equations. A major step in one of our characterizations is to show a version of the famous Niiro-Sawashima theorem for eventually positive operators. Several proofs for positive operators and semigroups do not work in our setting any longer, necessitating different arguments and giving our approach a distinct flavour.
