Geodesic
An integral formula for entropy of doubly stochastic operators
Bartosz Frej1 ; Paulina Frej1
1Institute 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

Voir la notice de l'article

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 
@article{10_4064_fm213_3_6,
     author = {Bartosz Frej and Paulina Frej},
     title = {An integral formula for entropy of
 doubly stochastic operators},
     journal = {Fundamenta Mathematicae},
     pages = {271--289},
     year = {2011},
     volume = {213},
     number = {3},
     doi = {10.4064/fm213-3-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm213-3-6/}
}
TY  - JOUR
AU  - Bartosz Frej
AU  - Paulina Frej
TI  - An integral formula for entropy of
 doubly stochastic operators
JO  - Fundamenta Mathematicae
PY  - 2011
SP  - 271
EP  - 289
VL  - 213
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm213-3-6/
DO  - 10.4064/fm213-3-6
LA  - en
ID  - 10_4064_fm213_3_6
ER  - 
%0 Journal Article
%A Bartosz Frej
%A Paulina Frej
%T An integral formula for entropy of
 doubly stochastic operators
%J Fundamenta Mathematicae
%D 2011
%P 271-289
%V 213
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/fm213-3-6/
%R 10.4064/fm213-3-6
%G en
%F 10_4064_fm213_3_6
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

Cité par Sources :