Preservers of Triple Transition Pseudo-Probabilities in Connection with Orthogonality Preservers and Surjective Isometries

Abstract We prove that every bijection preserving triple transition pseudo-probabilities between the sets of minimal tripotents two atomic JBW $$^*$$ ∗ -triples automatically preserves orthogonality in both directions. Consequently, each is precisely restriction a (complex-)linear isomorphism corresponding -triples. This result can be regarded as version celebrated Wigner theorem for symmetries on posets projections B ( H ). also present Tingley type by proving surjective isometry admits an extension to real linear these show class isometries is, general, strictly wider than set bijections pseudo-probabilities.