English

Operators on anti-dual pairs: Generalized Schur complement

Functional Analysis 2020-02-06 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2002.01714,
  title  = {Operators on anti-dual pairs: Generalized Schur complement},
  author = {Zsigmond Tarcsay and Tamás Titkos},
  journal= {arXiv preprint arXiv:2002.01714},
  year   = {2020}
}

Comments

15 pages

R2 v1 2026-06-23T13:31:44.806Z