English

On the operator equation AX-XB=C

Functional Analysis 2025-10-28 v1

Abstract

This work studies how certain problems in quantum theory have motivated some recent research in pure Mathematics in matrix and operator theory. The mathematical key is that of a commutator or a generalized commutator, that is, find an operator XB(H)X\in B(H) satisfying the operator equation AXXB=CAX - XB = C. By this we will show how and why to solve the operator equation AXXB=CAX - XB = C. As application we recall the solurion of AXBCXD=EAXB-CXD=E and we use the solution of this equation to solve equation of Monkeypox Diseases.

Cite

@article{arxiv.2510.21752,
  title  = {On the operator equation AX-XB=C},
  author = {Salah Mecheri and Ahmed Bachie and A. Segress},
  journal= {arXiv preprint arXiv:2510.21752},
  year   = {2025}
}
R2 v1 2026-07-01T07:04:32.125Z