Abstract In [Rahimi, M.: Entropy as an integral operator, Math. Slovaca 69(1) (2019), 139–146], we assigned an integral operator on a Hilbert space to any topological dynamical system of finite entropy and stated the entropy of the system in terms of the spectrum of the defined operator. Unfortunately, there is a mistake in the proof of the main theorem of the paper which makes the result incorrect. So, we can not extract the entropy of a topological dynamical system in terms of the spectrum of the introduced operator. In this note, we modify the main theorem of [11] by giving a modification to the proof of the theorem. Then, replacing the integral operator introduced in [11] by another linear operator, we will state the entropy of the system in terms of the spectrum of the new operator.

中文翻译：

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熵作为积分算子：勘误和修改

摘要在 [Rahimi, M.: Entropy as an integer operator, Math. Slovaca 69(1) (2019), 139–146]，我们将希尔伯特空间上的积分算子分配给任何有限熵的拓扑动力系统，并根据定义的算子的谱来说明系统的熵。不幸的是，论文主要定理的证明存在错误，导致结果不正确。因此，我们无法根据引入算子的频谱来提取拓扑动力系统的熵。在这篇笔记中，我们通过修改定理的证明来修改 [11] 的主要定理。然后，用另一个线性算子代替[11]中引入的积分算子，我们将根据新算子的谱来表示系统的熵。