Displaying similar documents to “ E φ , ϕ operators between normed spaces”

Operator entropy inequalities

M. S. Moslehian, F. Mirzapour, A. Morassaei (2013)

Colloquium Mathematicae

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We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting S q f ( A | B ) : = ∑ j = 1 n A j 1 / 2 ( A j - 1 / 2 B j A j - 1 / 2 ) q f ( A j - 1 / 2 B j A j - 1 / 2 ) A j 1 / 2 , and then give upper and lower bounds for S q f ( A | B ) as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004),...

On quantum informational thermodynamics with macrostates defined with respect to several operators

Bolesław Szafnicki

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CONTENTSINTRODUCTION.................................................................................................................................................................................. 5Chapter 1. PRELIMINARIES.............................................................................................................................................................. 7§ 1.1. Basic concepts of quantum mechanics.................................................................................................................................

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...

Symbolic extensions for nonuniformly entropy expanding maps

David Burguet (2010)

Colloquium Mathematicae

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A nonuniformly entropy expanding map is any ¹ map defined on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a r nonuniformly entropy expanding map T with r > 1 has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T. Downarowicz and A. Maass [Invent. Math. 176 (2009)].

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 local approach to g -entropy

Mehdi Rahimi (2015)

Kybernetika

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In this paper, a local approach to the concept of g -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of g -entropy.

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.

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.

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. ...