论文标题
本地运算符的光谱特性
Spectral properties of locally eventually positive operator semigroups
论文作者
论文摘要
本文认为，在本地正面阳性的Banach Lattices上，操作员的持续连续的半群是在混凝土四阶进化方程式中首次研究的属性。我们构建了一个简单的例子，以表明在文献中当前考虑的半群生成器的频谱上的典型假设在局部最终阳性的更一般环境中远非必要。在最小的其他假设下，我们获得了轨道渐近行为的结果，以及在局部最终阳性半群的外围点光谱上的必要条件。
This paper considers strongly continuous semigroups of operators on Banach lattices which are locally eventually positive, a property that was first investigated in the context of concrete fourth-order evolution equations. We construct a simple example to show that the typical assumptions on the spectrum of the semigroup generator considered currently in the literature are far from necessary in the more general setting of local eventual positivity. Under minimal additional assumptions, we obtain results on the asymptotic behaviour of orbits, as well as necessary conditions on the peripheral point spectrum of locally eventually positive semigroups.
