Lajos Molnar: On a parametric family of distance measures that includes the Hellinger and the Bures distances
We define a parametric family of certain two-variable functions on positive cones of C*-algebras that can be considered as a family of potential distance measures including the well-known Hellinger and Bures metrics. We study that family from various points of view. The main questions concern the problem of the well-definedness of the elements of the family, and, whenever we have an affirmative answer to that question, the problem of whether those distance measures are true metrics. Besides, we obtain some related trace characterizations. Our study is far from complete, we formulate several probably quite difficult open questions.
Roman Drnovšek in Primož Moravec