Document Type
Article
Publication Date
2-15-2018
Abstract
After outlining the way in which an intrinsic mean G={Gn} on a complete metric space gives rise to a contractive barycentric map on some class of Borel probability measures and some basic examples of this process, we show how the resulting barycentric map gives rise to a general theory of integration of measurable functions into the space. We apply this machinery to the cone of positive invertible elements of a C⁎-algebra equipped with the Thompson metric to derive barycentric maps and their basic properties arising from the power means. Finally we derive basic results for the Karcher barycenter including its approximation by the barycentric maps for power means and its satisfaction of the Karcher equation.
Publication Source (Journal or Book title)
Journal of Mathematical Analysis and Applications
First Page
1009
Last Page
1026
Recommended Citation
Kim, S., Lawson, J., & Lim, Y. (2018). Barycentric maps for compactly supported measures. Journal of Mathematical Analysis and Applications, 458 (2), 1009-1026. https://doi.org/10.1016/j.jmaa.2017.09.037