TY - JOUR
AB - We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.
AU - Virosztek, Daniel
ID - 405
JF - Linear Algebra and Its Applications
TI - Jointly convex quantum Jensen divergences
VL - 576
ER -
TY - JOUR
AB - Borel probability measures living on metric spaces are fundamental
mathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere.
AU - Virosztek, Daniel
ID - 284
IS - 1-2
JF - Acta Scientiarum Mathematicarum (Szeged)
TI - Maps on probability measures preserving certain distances - a survey and some new results
VL - 84
ER -