English

Wigner's theorem revisited

Classical Analysis and ODEs 2012-11-27 v1

Abstract

In this paper, we give the general solution of the functional equation {f(x)+f(y),f(x)f(y)}={x+y,xy}(x,yX)\big\{\|f(x)+f(y)\|,\|f(x)-f(y)\|\big\}=\big\{\|x+y\|,\|x-y\|\big\}\qquad(x,y\in X) where f:XYf:X\to Y and X,YX,Y are inner product spaces. Related equations are also considered. Our main tool is a real version of Wigner's unitary--antiunitary theorem.

Keywords

Cite

@article{arxiv.1211.4600,
  title  = {Wigner's theorem revisited},
  author = {Gyula Maksa and Zsolt Páles},
  journal= {arXiv preprint arXiv:1211.4600},
  year   = {2012}
}
R2 v1 2026-06-21T22:41:15.546Z