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/