论文标题
Stinespring的无限运营商定理有价值的本地完全积极地图及其应用
Stinespring's Theorem for Unbounded Operator valued Local completely positive maps and Its Applications
论文作者
论文摘要
Anar A. Dosiev在[本地操作员空间，无界操作员和多构型$ C^*$ - 代数，J。Funct。肛门。 255（2008），1724-1760]在本地$ c^{\ ast} $ - 代数上获得了局部完全正面地图的Stinespring定理（简而言之：本地CP-MAPS）。在本文中，已经确定了适当的最小化概念，以确保与相关表示形式达到单一等效性的唯一性。已证明，使用此ra nikodym类型定理用于局部完全正面地图。 此外，在本地$ c^{\ ast} $ - 代数（也称为本地CP诱导地图）上，对无界操作员的stinespring定理重视了希尔伯特模块上的本地完全正面地图。构造M.joiţa后，已经显示了用于局部CP诱导地图的ra型 - 尼克比型定理。在这两种情况下，获得的ra子衍生物是在某些复杂的希尔伯特空间上获得的正收缩，并具有向上过滤的还原子空间家族。
Anar A. Dosiev in [Local operator spaces, unbounded operators and multinormed $C^*$-algebras, J. Funct. Anal. 255 (2008), 1724-1760], obtained a Stinespring's theorem for local completely positive maps (in short: local CP-maps) on locally $C^{\ast}$-algebras. In this article a suitable notion of minimality for this construction has been identified so as to ensure uniqueness up to unitary equivalence for the associated representation. Using this a Radon-Nikodym type theorem for local completely positive maps has been proved. Further, a Stinespring's theorem for unbounded operator valued local completely positive maps on Hilbert modules over locally $C^{\ast}$-algebras (also called as local CP-inducing maps) has been presented. Following a construction of M. Joiţa, a Radon-Nikodym type theorem for local CP-inducing maps has been shown. In both cases the Radon-Nikodym derivative obtained is a positive contraction on some complex Hilbert space with an upward filtered family of reducing subspaces.
