Completely positive maps, weak log-majorization, determinantal inequalities, Positive definite matrices


Let $\Phi:\bM_n\to\bM_n$ be a unital trace preserving completely positive map and $A\in\bM_n$ be a positive definite matrix. Weak log-majorization and weak majorization between $\Phi(A)$ and $A$ are studied. Determinantal inequalities between $\Phi(A)$ and $A$ are obtained as a consequence. By considering special classes of unital trace preserving completely positive map, some known matrix inequalities such as Fischer's inequality are rediscovered. An affirmative answer to a question of Tam and Zhang in 2019 is given.

abs_vol35_pp524-532.pdf (116 kB)

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