Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 42 – 55
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0122
On norms of derivations implemented by self-adjoint operators
Obogi Robert Karieko\(^{1}\)
\(^{1}\) Department of Mathematics and Actuarial Science, Kisii University, P.O BOX 408-40200, KISII, KENYA
Copyright © 2023 Obogi Robert Karieko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 17, 2023 – Accepted: June 16, 2023 – Published: June 30, 2023
Abstract
In this paper, we concentrate on norms of derivations implemented by self-adjoint operators. We determine the upper and lower norm estimates of derivations implemented by self-adjoint operators.The results show that the knowledge of self-adjoint governs the quantum chemical system in which the eigenvalue and eigenvector of a self-adjoint operator represents the ground state energy and the ground state wave function of the system respectively.
Keywords:
norm; orthogonality; self-adjoint operator; derivation; linear operator.