Order type relations on the set of tripotents in a JB*-triple Hamhalter, Jan Kalenda, Ondrej F. K. Peralta Pereira, Antonio Miguel We introduce, investigate and compare several order type relations on the set of tripotents in a JB∗ -triple. The main two relations we address are ≤h and ≤n. We write u ≤h e (or u ≤n e) if u is a self-adjoint (or normal) element of the Peirce-2 subspace associated to e considered as a unital JB∗ -algebra with unit e. It turns out that these relations need not be transitive, so we consider their transitive hulls as well. Properties of these transitive hulls appear to be closely connected with types of von Neumann algebras, with the results on products of symmetries, with determinants in finite-dimensional Cartan factors, with finiteness and other structural properties of JBW∗ -triples. 2025-10-24T11:36:22Z 2025-10-24T11:36:22Z 2025-10-06 journal article Hamhalter, J., Kalenda, O. F. K., & Peralta, A. M. (2025). Order type relations on the set of tripotents in a JB∗-triple. Dissertationes Mathematicae (Rozprawy Matematyczne), 78 pp.-78 pp. https://doi.org/10.4064/dm231004-6-5 https://hdl.handle.net/10481/107427 10.4064/dm231004-6-5 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Institute of Mathematics, Polish Academy of Sciences