论文标题
Loewner的定理用于操作域上的地图
Loewner's theorem for maps on operator domains
论文作者
论文摘要
经典的Loewner定理指出，在上半平面上的霍明型函数描述了操作员单调在实际间隔上的函数。我们通过广义上半平面的生物形态自动形态表征了局部秩序同构，这是所有具有积极可逆性假想部分的操作员的集合。我们以明确的方式描述了此类地图，并检查最大局部秩序同构的特性。此外，在有限尺寸的情况下，我们证明矩阵域的每个顺序嵌入是同构阶同构上的同构型，上面是在另一个矩阵域上。
The classical Loewner's theorem states that operator monotone functions on real intervals are described by holomorphic functions on the upper half-plane. We characterize local order isomorphisms on operator domains by biholomorphic automorphisms of the generalized upper half-plane, which is the collection of all operators with positive invertible imaginary part. We describe such maps in an explicit manner, and examine properties of maximal local order isomorphisms. Moreover, in the finite-dimensional case, we prove that every order embedding of a matrix domain is a homeomorphic order isomorphism onto another matrix domain.
