论文标题
操作员凹功能的分析提升
Analytic lifts of operator concave functions
论文作者
论文摘要
本文背后的动机是三倍。首先，研究，表征和实现操作员凹陷及其应用于操作员在操作范围内的单调性，而这些功能在运算符域上的单调性不被假定为矩阵凸。其次，使用所获得的基于Schur补体的表示公式来分析概率措施的操作手段，并通过随机变量强调其研究。第三，以体面的一般性获得这些结果。也就是说，对于$ \ Mathcal {a} \ otimes \ Mathcal {b}（e）$的任意张量产品空间中的域，其中$ \ Mathcal {a} $是Banach Space，$ \ Mathcal {b}（b}（e）$表示边界的线性linearear opertors a flineD linear opertors a hillbert $ e $ e $ e $ e $ e。当$ \ Mathcal {a} $只是本地凸空间时，我们的参数也适用。
The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix convex. Secondly, to use the obtained Schur complement based representation formulas to analytically extend operator means of probability measures and to emphasize their study through random variables. Thirdly, to obtain these results in a decent generality. That is, for domains in arbitrary tensor product spaces of the form $\mathcal{A}\otimes\mathcal{B}(E)$, where $\mathcal{A}$ is a Banach space and $\mathcal{B}(E)$ denotes the bounded linear operators over a Hilbert space $E$. Our arguments also apply when $\mathcal{A}$ is merely a locally convex space.
