Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64863We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.13 pages, To appear in J. Funct. AnalFunctional AnalysisQuantum PhysicsOrthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theoremtext