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.
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页码：125 / 143
页数：19
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