Operators on anti-dual pairs: Generalized Schur complement

被引：2

作者：

Tarcsay, Zsigmond ^{[1
]}

Titkos, Tamas ^{[2
,3
]}

机构：

[1] Eotvos Lorand Univ, Dept Appl Anal & Computat Math, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

[2] Alfred Renyi Inst Math, Realtanoda Utca 13-15, H-1053 Budapest, Hungary

[3] BBS Univ Appl Sci, Alkotmany U 9, H-1054 Budapest, Hungary

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 614卷 / 614期

关键词：

Positive operator; Anti-duality; Schur complement; Parallel sum; Parallel difference; Rigged Hilbert space; *-Algebra;

D O I：

10.1016/j.laa.2020.02.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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. (C) 2020 The Authors. Published by Elsevier Inc.

引用

页码：125 / 143

页数：19

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