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- W2783247317 abstract "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*} Phi ^{p} big(A nabla _{v} B+2 r Mm (A^{-1}nabla B^{-1}- &A^{-1} sharp B^{-1} & leq left( frac{K(h)}{ 4^{frac{2}{p}-1} K^{r_{1}} left( sqrt {h^{'}}right)} right) ^{p} Phi^{p} (A sharp_{nu} B) end{align*} and begin{align*} Phi ^{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} (Phi(A) sharp_{nu} Phi (B))^{p}, end{align*} where $Phi$ is a positive unital linear map, $ 0 leq nu leq 1$, $p geq 2,$ $r=min{nu,1-nu},$ $h=frac{M}{m},$ $h^{'}=frac{M^{'}}{m^{'}}$, $K(h)=frac{(1+h)^{2}}{4h}$ and $r_{1}=min{2r,1-2r}.$ We also obtain a reverse of the Ando inequality for positive linear maps via the Kantorovich constant." @default.
- W2783247317 created "2018-01-26" @default.
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- W2783247317 date "2018-01-06" @default.
- W2783247317 modified "2023-09-27" @default.
- W2783247317 title "Improvements of some operator inequalities involving positive linear maps via the Kantorovich constant" @default.
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