Inequalities Between Eigenvalues, Entropy Numbers, and Related Quantities of Compact Operators in Banach Spaces.
Bernd Carl, Hans Triebel (1980)
Mathematische Annalen
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Bernd Carl, Hans Triebel (1980)
Mathematische Annalen
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D.E. Edmunds, H. Triebel (1994)
Mathematische Annalen
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Bernd Carl (1989)
Banach Center Publications
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Carl, Bernd, Edmunds, David E. (2001)
Journal of Inequalities and Applications [electronic only]
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Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Bartosz Frej (2006)
Fundamenta Mathematicae
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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.
Bartosz Frej, Paulina Frej (2011)
Fundamenta Mathematicae
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A new formula for entropy of doubly stochastic operators is presented. It is also checked that this formula fulfills the axioms of the axiomatic definition of operator entropy, introduced in an earlier paper of Downarowicz and Frej. As an application of the formula the 'product rule' is obtained, i.e. it is shown that the entropy of a product is the sum of the entropies of the factors. Finally, the proof of continuity of the new 'static' entropy as a function of the measure is given. ...
Bernd Carl, Thomas Kühn (1985)
Revista Matemática Iberoamericana
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In the paper local entropy moduli of operators between Banach spaces are introduced. They constitue a generalization of entropy numbers and moduli, and localize these notions in an appropriate way. Many results regarding entropy numbers and moduli can be carried over to local entropy moduli. We investigate relations between local entropy moduli and s-numbers, spectral properties, eigenvalues, absolutely summing operators. As applications, local entropy moduli of identical and diagonal...
Bernd Carl, Irmtraud Stephani (1984)
Journal für die reine und angewandte Mathematik
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Fumio Hiai, Dénes Petz (2007)
Banach Center Publications
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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
Brunon Kamiński, José de Sam Lazaro (2000)
Colloquium Mathematicae
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We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.
Chakrabarti, C.G., De, Kajal (2000)
International Journal of Mathematics and Mathematical Sciences
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Inder Jeet Taneja (1977)
Annales Polonici Mathematici
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Kyewon Koh Park, Uijung Lee (2004)
Studia Mathematica
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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.
Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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