arXiv subjects
Publications and source records attributed to Leila Nasiri.
In this paper, we give new singular value inequalities and determinant inequalities including the inverse of $A$, $B$ and $A+B$ for sector matrices. We also give the matrix inequalities for sector matrices with a positive multilinear map. Our obtained results give generalizations for the known results.
In this short paper, we establish a reverse of the derived inequalities for sector matrices by Tan and Xie, with Kantorovich constant. Then, as application of our main theorem, some inequalities for determinant and unitarily invariant norm are presented.
We present some operator inequalities for positive linear maps that generalize and improve the derived results in some recent years. For instant, if $A$ and $B$ are positive operators and $m,m^{'},M,M^{'}$ are positive real numbers satisfying either one of the condition $ 0<m \leq B \leq m^{'} <M^{'} \leq A \leq M $ or $0<m \leq A \leq m^{'} <M^{'} \leq B \leq M$, then \begin{align*} Φ^{p} \big(A \nabla _{v} B+2 r Mm (A^{-1}\nabla B^{-1}- &A^{-1} \sharp B^{-1} )\big)\\ & \leq \left( \frac{K(h)}{ 4^{\frac{2}{p}-1} K^{r_{1}} \left( \sqrt {h^{'}}\right)} \right) ^{p} Φ^{p} (A \sharp_ν B) \end{align*} and \begin{align*} Φ^{p} \big(A \nabla _{v} B+2 r Mm (A^{-1}\nabla B^{-1}-& A^{-1} \sharp B^{-1} )\big) \\ &\leq \left( \frac{K(h)}{ 4^{\frac{2}{p}-1} K^{r_{1}}\left( \sqrt {h^{'}}\right)}\right) ^{p} (Φ(A) \sharp_ν Φ(B))^{p}, \end{align*} where $Φ$ is a positive unital linear map, $ 0 \leq ν\leq 1$, $p \geq 2,$ $r=\min\{ν,1-ν\},$ $h=\frac{M}{m},$ $h^{'}=\frac{M^{'}}{m^{'}}$, $K(h)=\frac{(1+h)^{2}}{4h}$ and $r_{1}=\min\{2r,1-2r\}.$ We also obtain a reverse of the Ando inequality for positive linear maps via the Kantorovich constant.