论文标题
反对偶对的操作员：自偶会扩展和强大的帕罗特定理
Operators on anti-dual pairs: self-adjoint extensions and the Strong Parrott Theorem
论文作者
论文摘要
本文的目的是开发一种方法，以获取作用于反对偶对的对称操作员的自我伴侣扩展。这种结果的主要优点是它可以应用于不携带希尔伯特空间结构或规范拓扑结构的结构。实际上，我们将展示如何通过其诱导的操作员来支配参与代数的线性功能的遗传性扩展。作为运营商的理论应用程序，我们直接概括了帕罗特定理，即$ 2 $乘$ 2 $ 2 $块运营商价值矩阵。为了在非交通集成中展示适用性，我们表征了在$ c^{*} $ - 代数的左侧理想中定义的对称功能的Hermitian扩展性。
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space structure or a normable topology. In fact, we will show how hermitian extensions of linear functionals of involutive algebras can be governed by means of their induced operators. As an operator theoretic application, we provide a direct generalization of Parrott's theorem on contractive completion of $2$ by $2$ block operator-valued matrices. To exhibit the applicability in noncommutative integration, we characterize hermitian extendibility of symmetric functionals defined on a left ideal of a $C^{*}$-algebra.
