An integral formula for entropy of doubly stochastic operators

Tom 213 / 2011

Bartosz Frej, Paulina Frej Fundamenta Mathematicae 213 (2011), 271-289 MSC: Primary 28D20; Secondary 47A35. DOI: 10.4064/fm213-3-6

Streszczenie

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.

Autorzy

  • Bartosz FrejInstitute of Mathematics and Informatics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Paulina FrejInstitute of Mathematics and Informatics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek