反对偶对上的算子：广义Schur补
Operators on anti-dual pairs: Generalized Schur complement
摘要：
本文的目的是发展Schur互补理论的背景下，运营商的反对偶对。作为一个副产品，我们得到了一个自然的推广的并行和和并行差，以及Lebesgue型分解。为了说明这种算子方法在应用中的工作原理，我们得到了相应的结果，运营商的操纵希尔伯特空间，并表示泛函的${}^{*}$ -代数。
英文摘要：
The goal of this paper is to develop the theory of Schur complementation in the context of operators acting on anti-dual pairs. As a byproduct, we obtain a natural generalization of the parallel sum and parallel difference, as well as the Lebesgue-type decomposition. To demonstrate how this operator approach works in application, we derive the corresponding results for operators acting on rigged Hilbert spaces, and for representable functionals of ${}^{*}$-algebras.
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