An integral formula for entropy of doubly stochastic operators

• Autorzy: Bartosz Frej , Paulina Frej
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A35: Ergodic theory
• 28D20: Entropy and other invariants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 3
• Strony: 271-289

Daty

wydano

2011

Twórcy

autor

Bartosz Frej

• Institute of Mathematics and Informatics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Paulina Frej

• Institute of Mathematics and Informatics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/fm213-3-6