On Self-Adjoint Linear Relations

DOI10.1556/314.2020.00001zbMATH Open1474.47007arXiv1902.10518OpenAlexW3163283407MaRDI QIDQ4997629

Author name not available (Why is that?)

Publication date: 29 June 2021

Published in: (Search for Journal in Brave)

Abstract: A linear operator on a Hilbert space $mathbbH$, in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be ommited by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if $k+l:k,linG(S)capG(S{)}^{*}=mathbbH$. In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.

Full work available at URL: https://arxiv.org/abs/1902.10518

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: On Self-Adjoint Linear Relations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4997629)