论文标题
积极操作员的多个良好性增加了功能的支持
Aperiodicity of positive operators that increase the support of functions
论文作者
论文摘要
考虑一个正面运算符$ t $在$ l^p $ -space（或更一般而言的Banach晶格）上，从而增加了功能的支持，从$ supp（tf）\ supseteq supp {f} $ for every函数$ f \ ge ge 0 $。我们表明，这意味着在温和的假设下，$ t $没有单模型的特征值，除了可能的$ 1 $。这排除了$ t $的任何轨道的周期性行为，因此使我们能够在许多情况下证明这些权力的融合。 为了证明，我们首先对晶格同态对功能支持的作用进行仔细分析；然后，我们将$ t $分为可逆和稳定的零件，并将上述分析应用于可逆零件。对该论点的适当适应使我们能够证明我们的主要结果的另一个版本，这对于研究所谓的不可还原运营商很有用。
Consider a positive operator $T$ on an $L^p$-space (or, more generally, a Banach lattice) which increases the support of functions in the sense that $supp(Tf) \supseteq supp{f}$ for every function $f \ge 0$. We show that this implies, under mild assumptions, that $T$ has no unimodular eigenvalues except for possibly the number $1$. This rules out periodic behaviour of any orbits of the powers of $T$, and thus enables us to prove convergence of those powers in many situations. For the proof we first perform a careful analysis of the action of lattice homomorphisms on the support of functions; then we split $T$ into an invertible and a weakly stable part, and apply the aforementioned analysis to the invertible part. An appropriate adaptation of this argument allows us to prove another version of our main result which is useful for the study of so-called irreducible operators.
