کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5774953 1413571 2017 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces
چکیده انگلیسی
We extend Ando-Hiai's log-majorization for the weighted geometric mean of positive definite matrices into that for the Cartan barycenter in the general setting of probability measures on the Riemannian manifold of positive definite matrices equipped with trace metric. The main key is the settlement of the monotonicity problem of the Cartan barycenteric map on the space of probability measures with finite first moment for the stochastic order induced by the cone. We also derive a version of Lie-Trotter formula and related unitarily invariant norm inequalities for the Cartan barycenter as the main application of log-majorization.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 453, Issue 1, 1 September 2017, Pages 195-211
نویسندگان
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