Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774479 | Journal of Mathematical Analysis and Applications | 2017 | 21 Pages |
Abstract
Let C be an open cone in a Banach space equipped with the Thompson metric with closure a normal cone. The main result gives sufficient conditions for Borel probability measures μ,ν on C with finite first moment for which μâ¤Î½ in the stochastic order induced by the cone to be order approximated by sequences {μn}, {νn} of uniform finitely supported measures in the sense that μnâ¤Î½n for each n and μnâμ, νnâν in the Wasserstein metric. This result is the crucial tool in developing a pathway for extending various inequalities on operator and matrix means, which include the harmonic, geometric, and arithmetic operator means on the cone of positive elements of a Câ-algebra, to the space P1(C) of Borel measures of finite first moment on C. As an illustrative and important particular application, we obtain the monotonicity of the Karcher geometric mean on P1(A+) for the positive cone A+ of a Câ-algebra A.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jimmie Lawson,