Wigner-Type Theorems for Projections
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.
KeywordsOrthomodular poset Lattices of subspaces Wigner’s theorem
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