Entropy as an integral operator: Erratum and modification
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Mehdi Rahimi
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.
(Communicated by Marcus Waurick)
Acknowledgement
The author would like to thank the referees for their comprehensive and useful comments which helped the improvement of this work to the present form.
References
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© 2020 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- Monadic pseudo BE-algebras
- Quadruple construction of decomposable double MS-algebras
- Fibonacci numbers in generalized Pell sequences
- Solutions of a generalized markoff equation in Fibonacci numbers
- Root separation for polynomials with reducible derivative
- Quadratic refinements of Young type inequalities
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
- Integration with respect to deficient topological measures on locally compact spaces
- Differential subordinations and Pythagorean means
- Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
- Unbounded oscillation of fourth order functional differential equations
- Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
- Entropy as an integral operator: Erratum and modification
- Unital topology on a unital l-group
- On the topological complexity of Grassmann manifolds
- Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
- Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
- Two semigroup rings associated to a finite set of meromorphic functions
