Maps on self-adjoint operators preserving some relations related to commutativity
Functional Analysis
2024-02-15 v1
Abstract
In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both directions. We show that those maps are implemented by unitary or antiunitary equivalence and possible additive perturbation by a scalar operator.
Cite
@article{arxiv.2402.09227,
title = {Maps on self-adjoint operators preserving some relations related to commutativity},
author = {Mahdi Karder and Tatjana Petek},
journal= {arXiv preprint arXiv:2402.09227},
year = {2024}
}