论文标题
与LIEB的功能和Minkowski类型操作员不等式相关的共同凸映射
Jointly convex mappings related to the Lieb's functional and Minkowski type operator inequalities
论文作者
论文摘要
Employing the notion of operator log-convexity, we study joint concavity$/$ convexity of multivariable operator functions: $(A,B)\mapsto F(A,B)=h\left[ Φ(f(A))\ σ Ψ(g(B))\right]$, where $Φ$ and $Ψ$ are positive linear maps and $σ$ is an operator mean.作为应用程序，我们证明了矩阵跟踪功能的共同凹面$/$凸度$ \ tr \ left \ {f（a，b）\ right \} $。 Moreover, considering positive multi-linear mappings in $F(A,B)$, our study of the joint concavity$/$ convexity of $(A_1,\cdots,A_k)\mapsto h\left[ Φ(f(A_1),\cdots,f(A_k))\right]$ provides some generalizations and complement to results of Ando and Lieb concerning the concavity$/$涉及张量产品的地图的凸度。此外，我们为单位正线性地图提供了Minkowski类型的操作员不等式，这是Minkowski类型矩阵跟踪不平等的运算符版本，而不是Carlen和Lieb，Bekjan，以及Ando and Hiai。
Employing the notion of operator log-convexity, we study joint concavity$/$ convexity of multivariable operator functions: $(A,B)\mapsto F(A,B)=h\left[ Φ(f(A))\ σ Ψ(g(B))\right]$, where $Φ$ and $Ψ$ are positive linear maps and $σ$ is an operator mean. As applications, we prove jointly concavity$/$convexity of matrix trace functions $\Tr\left\{ F(A,B)\right\}$. Moreover, considering positive multi-linear mappings in $F(A,B)$, our study of the joint concavity$/$ convexity of $(A_1,\cdots,A_k)\mapsto h\left[ Φ(f(A_1),\cdots,f(A_k))\right]$ provides some generalizations and complement to results of Ando and Lieb concerning the concavity$/$ convexity of maps involving tensor product. In addition, we present Minkowski type operator inequalities for a unial positive linear map, which is an operator version of Minkowski type matrix trace inequalities under a more general setting than Carlen and Lieb, Bekjan, and Ando and Hiai.
