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Mean Li-Yorke chaos in Banach spaces

机译：在Banach空间中的意思是Li-Yorke Chaos

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摘要

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only if it has an absolutely mean irregular vector. As a consequence, absolutely Cesaro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke chaos is shown to be equivalent to the existence of a dense (or residual) set of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained. Moreover, we construct an example of an invertible hypercyclic operator T such that every nonzero vector is absolutely mean irregular for both T and T-1. Several other examples are also presented. Finally, mean Li-Yorke chaos is also investigated for C-0-semigroups of operators on Banach spaces. (C) 2019 Elsevier Inc. All rights reserved.
机译：我们调查Banach空间上的运营商的平均亮度混乱的概念。我们表明它与2型类型的分布混乱的概念不同，与紧凑型度量空间上的拓扑动态背景下的情况相反。我们证明了操作员是卑鄙的，如果它具有绝对平均不规则的载体，则才能混乱。因此，绝对Cesaro有界经营者永远不会是李 - yorke混乱。致密的平均值Li-Yorke Chaos相当于存在致密（或残余）绝对平均不规则载体的存在。因此，每种均值李 - yorke混沌操作员在一些无限维闭合不变子空间上密度为李 - yorke混乱。 A（致密）是指Li-Yorke混沌标准以及还获得了存在绝对平均不规则歧管的充分条件。此外，我们构建可逆性的Hyperyclic操作员T的示例，使得每个非零矢量绝对是T和T-1的不规则。还提出了其他几个例子。最后，平均值在Banach空间上对运营商的C-0-Semigrous进行了调查。 （c）2019 Elsevier Inc.保留所有权利。

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