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- W4283662471 abstract "Let $phi$ be a linear map from the $ntimes n$ matrices ${mathcal M}_n$ to the $mtimes m$ matrices ${mathcal M}_m$. It is known that $phi$ is $2$-positive if and only if for all $Kin {mathcal M}_n$ and all strictly positive $Xin {mathcal M}_n$, $phi(K^*X^{-1}K) geq phi(K)^*phi(X)^{-1}phi(K)$. This inequality is not generally true if $phi$ is merely a Schwarz map. We show that the corresponding tracial inequality ${rm Tr}[phi(K^*X^{-1}K)] geq {rm Tr}[phi(K)^*phi(X)^{-1}phi(K)]$ holds for a wider class of positive maps that is specified here. We also comment on the connections of this inequality with various monotonicity that have found wide use in mathematical physics, and apply it, and a close relative, to obtain some new, definitive results." @default.
- W4283662471 created "2022-06-29" @default.
- W4283662471 creator A5035114804 @default.
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- W4283662471 date "2022-03-07" @default.
- W4283662471 modified "2023-09-23" @default.
- W4283662471 title "Characterizing Schwarz maps by tracial inequalities" @default.
- W4283662471 doi "https://doi.org/10.48550/arxiv.2203.03433" @default.
- W4283662471 hasPublicationYear "2022" @default.
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