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Keywords

positive linear maps, geometric mean, sector matrix, norm inequality

Abstract

Ando proved that if $A, B$ are positive definite, then for any positive linear map $\Phi$, it holds \begin{eqnarray*} \Phi(A\sharp_\lambda B)\le \Phi(A)\sharp_\lambda \Phi(B), \end{eqnarray*} where $A\sharp_\lambda B$, $0\le\lambda\le 1$, means the weighted geometric mean of $A, B$. Using the recently defined geometric mean for accretive matrices, Ando's result is extended to sector matrices. Some norm inequalities are considered as well.

abs_vol35_pp418-423.pdf (113 kB)
Abstract

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