紧凑算子的熵以及关于熵和规范的结果

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-17 DOI:arxiv-2409.10844

Paulo Lupatini, Felipe Silva, Régis Varão

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引用次数: 0

摘要

我们证明，对于作用于无限维$F$空间的算子，规范性质意味着无限拓扑熵。此外，我们还证明了作用于巴拿赫空间的紧凑算子表现出有限熵，并且熵完全取决于算子的点谱。此外，我们还证明了变分原理对于作用于巴拿赫空间的紧凑算子不成立。

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Entropy for compact operators and results on entropy and specification

We prove that the specification property implies infinite topological entropy for operators acting on infinite dimensional $F$-spaces. Furthermore, we establish compact operators acting on Banach spaces exhibit finite entropy and the entropy depends exclusively on the operator's point spectrum. Additionally, we prove that the variational principle does not hold for compact operators acting on Banach spaces.

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arXiv - MATH - Dynamical Systems

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