An integral formula for entropy of doubly stochastic operators

Bartosz Frej, and Paulina Frej. "An integral formula for entropy of doubly stochastic operators." Fundamenta Mathematicae 213.3 (2011): 271-289. <http://eudml.org/doc/282638>.

@article{BartoszFrej2011,
abstract = {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.},
author = {Bartosz Frej, Paulina Frej},
journal = {Fundamenta Mathematicae},
keywords = {doubly stochastic operator; Markov operator; entropy; product rule},
language = {eng},
number = {3},
pages = {271-289},
title = {An integral formula for entropy of doubly stochastic operators},
url = {http://eudml.org/doc/282638},
volume = {213},
year = {2011},
}

TY - JOUR
AU - Bartosz Frej
AU - Paulina Frej
TI - An integral formula for entropy of doubly stochastic operators
JO - Fundamenta Mathematicae
PY - 2011
VL - 213
IS - 3
SP - 271
EP - 289
AB - 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.
LA - eng
KW - doubly stochastic operator; Markov operator; entropy; product rule
UR - http://eudml.org/doc/282638
ER -