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Asymmetric Choi--Davis inequalities | | Mohsen Kian
; M. S. Moslehian
; R. Nakamoto
; | | Date: |
27 Jan 2020 | | Abstract: | Let $Phi$ be a unital positive linear map and let $A$ be a positive
invertible operator. We prove that there exist partial isometries $U$ and $V$
such that [ |Phi(f(A))Phi(A)Phi(g(A))|leq U^*Phi(f(A)Ag(A))U ] and
[left|Phileft(f(A)
ight)^{-r}Phi(A)^rPhileft(g(A)
ight)^{-r}
ight|leq
V^*Phileft(f(A)^{-r}A^rg(A)^{-r}
ight)V] hold under some mild operator
convex conditions and some positive numbers $r$. Further, we show that if $f^2$
is operator concave, then $$ |Phi(f(A))Phi(A)|leq Phi(Af(A)).$$ In
addition, we give some counterparts to the asymmetric Choi--Davis inequality
and asymmetric Kadison inequality. Our results extend some inequalities due to
Bourin--Ricard and Furuta. | | Source: | arXiv, 2001.9962 | | Services: | Forum | Review | PDF | Favorites | |
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