论文标题
地图保留了积极操作员的绝对连续性和奇异性
Maps preserving absolute continuity and singularity of positive operators
论文作者
论文摘要
在本文中，我们考虑了作用于无限尺寸，复杂的希尔伯特空间的所有正面，有限的操作员的锥体，并检查了在这两个方向上都保留绝对连续性的徒图。事实证明，这些地图正是在两个方向上都保留奇异性的地图。此外，从某种意义上说，这样的地图总是由基础希尔伯特空间的有限，可逆，线性或偶联的线性操作员引起的。我们的结果可能对最近的Molnar定理进行了概括，该定理表征了阳性锥体上的地图，从而保留了操作员的Lebesgue分解。
In this paper we consider the cone of all positive, bounded operators acting on an infinite dimensional, complex Hilbert space, and examine bijective maps that preserve absolute continuity in both directions. It turns out that these maps are exactly those that preserve singularity in both directions. Moreover, in some weak sense, such maps are always induced by bounded, invertible, linear- or conjugate linear operators of the underlying Hilbert space. Our result gives a possible generalization of a recent theorem of Molnar which characterizes maps on the positive cone that preserve the Lebesgue decomposition of operators.
