Home > ELA > Vol. 35 (2019)
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.
Recommended Citation
Tan, Fuping and Chen, Huimin.
(2019),
"Inequalities for sector matrices and positive linear maps",
Electronic Journal of Linear Algebra,
Volume 35, pp. 418-423.
DOI: https://doi.org/10.13001/1081-3810.4041
Abstract