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International Journal of Theoretical Physics

, Volume 47, Issue 1, pp 69–80 | Cite as

Wigner-Type Theorems for Projections

  • Georges Chevalier
Article

Abstract

The Wigner theorem, in its Uhlhorn’s formulation, states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex Hilbert space which preserves orthogonality is induced by either a unitary or an antiunitary operator. There exist in the literature many Wigner-type theorems and the purpose of this paper is to prove in an algebraic setting a very general Wigner-type theorem for projections (idempotent linear mappings). As corollaries, Wigner-type theorems for projections in real locally convex spaces, infinite dimensional complex normed spaces and Hilbert spaces are obtained.

Keywords

Orthomodular poset Lattices of subspaces Wigner’s theorem 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Georges Chevalier, Université Lyon 1, Institut Camille JordanVilleurbanne cedexFrance

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