Journal of the Australian Mathematical Society (Series A)

Research Article

An algebraic approach to Wigner's unitary-antiunitary theorem

Lajos Molnára1

a1 Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O.Box 12, Hungary e-mail: molnarl@math.klte.hu

Abstract

We present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert modules over matrix algebras. We also present a Wigner-type result for maps on prime C*-algebras.

(Received February 17 1998)

(Revised August 13 1998)

1991 Mathematics subject classification (Amer. Math. Soc.)

  • primary 46C05;
  • 46C50;
  • secondary 47D25;
  • 16N60

Keywords and phrases

  • Wigner's unitary-antiunitary theorem;
  • Hilbert module;
  • C*-algebra;
  • prime ring;
  • Jordan homomorphism