Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhornʹs Version of Wignerʹs Theorem

We present an analogue of Uhlhornʹs version of Wignerʹs 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.