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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. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of entropy kernel operator for compact dynamical systems of finite Kolmogorov entropy. It is a compact positive operator on a Hilbert space. Then we state the Kolmogorov entropy in terms of the eigenvalues of the entropy kernel operator. [ABSTRACT FROM AUTHOR]

In this paper, the concept of φ-entropy is defined and some of the its properties are proved. It is a type of generalized entropy with generalized properties. It is invariant under topological conjugacy and satisfies a generalized version of Jaccob's Theorem. Finally, we will extract the Kolmogorov entropy as a special case, by setting φ to be the identity function. [ABSTRACT FROM AUTHOR]

In this paper, a type of fuzzy entropy of action of a semi-group on a metric space is introduced. Then we apply this concept to specific semi-groups to state this entropy in terms of the known entropies. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of entropy operator for a continuous system of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If φ is invertible then the entropy operator is bounded by the topological entropy of φ as its norm. [ABSTRACT FROM AUTHOR]