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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-6,
author = {Bartosz Frej and Paulina Frej},
title = {An integral formula for entropy of doubly stochastic operators},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {271-289},
zbl = {1234.28019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-6}
}
Bartosz Frej; Paulina Frej. An integral formula for entropy of doubly stochastic operators. Fundamenta Mathematicae, Tome 215 (2011) pp. 271-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-6/