Geodesic
An integral formula for entropy of doubly stochastic operators
Bartosz Frej 1   ; Paulina Frej 1
1 Institute of Mathematics and Informatics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Fundamenta Mathematicae, Tome 213 (2011) no. 3, pp. 271-289 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm213-3-6
Keywords: formula entropy doubly stochastic operators presented checked formula fulfills axioms axiomatic definition operator entropy introduced earlier paper downarowicz frej application formula product rule obtained shown entropy product sum entropies factors finally proof continuity static entropy function measure given

Bartosz Frej  1   ; Paulina Frej  1

1 Institute of Mathematics and Informatics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Bartosz Frej; Paulina Frej. An integral formula for entropy of
 doubly stochastic operators. Fundamenta Mathematicae, Tome 213 (2011) no. 3, pp. 271-289. doi: 10.4064/fm213-3-6

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