Displaying similar documents to “Entropy and n-widths of operators in Banach spaces”

Local entropy moduli and eigenvalues of operators in Banach spaces.

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...

Maličky-Riečan's entropy as a version of operator entropy

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.

Entropy pairs of ℤ² and their directional properties

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.

An integral formula for entropy of doubly stochastic operators

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. ...

The entropy conjecture for diffeomorphisms away from tangencies

Gang Liao, Marcelo Viana, Jiagang Yang (2013)

Journal of the European Mathematical Society

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We prove that every C 1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive. ...

A new approach to mutual information. II

Fumio Hiai, Takuho Miyamoto (2010)

Banach Center Publications

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A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.

A note on the entropy of a doubly stochastic operator

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.