The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-2-7, author = {Bartosz Frej}, title = {Mali\v cky-Rie\v can's entropy as a version of operator entropy}, journal = {Fundamenta Mathematicae}, volume = {189}, year = {2006}, pages = {185-193}, zbl = {1092.37004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-2-7} }
Bartosz Frej. Maličky-Riečan's entropy as a version of operator entropy. Fundamenta Mathematicae, Tome 189 (2006) pp. 185-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-2-7/