Completely positive mappings and mean matrices

Details Completely positive mappings and mean matrices Completely positive mappings and mean matrices

2010-12-21

arxiv.org/abs/1012.4754v1

Mathematics

Functional Analysis

15 pages

Scientific paper

Some real functions f induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define linear mapping beta on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of beta in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.

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