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An algebraic approach to Wigner's unitary-antiunitary theorem

Part of: Normed linear spaces and Banach spaces; Banach lattices Radicals and radical properties of rings

Published online by Cambridge University Press:  09 April 2009

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

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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.

Keywords

Wigner's unitary-antiunitary theoremHilbert moduleC*-algebraprime ringJordan homomorphism

MSC classification

Secondary: 46C05: Hilbert and pre-Hilbert spaces 46C50: Generalizations of inner products (semi-inner products, partial inner products, etc.) 16N60: Prime and semiprime rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 3 , December 1998 , pp. 354 - 369
Copyright
Copyright © Australian Mathematical Society 1998

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