论文标题
正面运算符的订单界限和顺序连续性属性
Order boundedness and order continuity properties of positive operator semigroups
论文作者
论文摘要
Kandić，Kramar-Fijavž和第二名的作者最近引入和研究了相对均匀的连续（RUC）半群，以使在矢量晶格的设置中可用的单参数运算符的理论理论，而通常不存在正常情况。 在本文中，我们返回到更为标准的Banach晶格设置（RUC Semigroups和$ c_0 $ $ semigroups都是定义明确的概念），并比较了这两个概念。我们表明，RUC半群恰好是那些正面旋转订单的正面$ C_0 $ -Semigroups。 然后，我们将此结果与三个不同的主题联系起来：（i）光谱平等和以$ c_0 $ semigroups为正的增长； （ii）一个统一的有限原则，该原则适用于Banach Lattices之间的所有操作员家庭； （iii）对无界顺序收敛的描述几乎是网络的任何地方收敛，而网中具有包含共序序列的无数索引集。
Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandić, Kramar-Fijavž, and the second-named author, in order to make the theory of one-parameter operator semigroups available in the setting of vector lattices, where no norm is present in general. In this article, we return to the more standard Banach lattice setting - where both ruc semigroups and $C_0$-semigroups are well-defined concepts - and compare both notions. We show that the ruc semigroups are precisely those positive $C_0$-semigroups whose orbits are order bounded for small times. We then relate this result to three different topics: (i) equality of the spectral and the growth bound for positive $C_0$-semigroups; (ii) a uniform order boundedness principle which holds for all operator families between Banach lattices; and (iii) a description of unbounded order convergence in terms of almost everywhere convergence for nets which have an uncountable index set containing a co-final sequence.
