arXiv subjects

Samuel Tiersma

Publications and source records attributed to Samuel Tiersma.

3 recordsLinked to original sources

arXiv2026

On the Shirshov--Cohn theorem for JB-algebras

It is shown that a JB-algebra which can be generated by the union of two of its associative Jordan subalgebras is a JC-algebra, hence special. A similar refinement of Macdonald's principle for JB-algebras is obtained. Moreover, we prove that the free unital JB-algebra generated by $n$ projections is a JC-algebra if and only if $n\in \{1,2,3\}$. Finally, we give an explicit description of the free unital JB-algebra generated by two projections paralleling the Raeburn-Sinclair theorem for C*-algebras.

math.OA↗

arXiv2026

An order-theoretic characterization of C*-algebras

We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems. It is based on the characterization of JB-algebras among the order unit spaces in terms of the existence of gauge-reversing bijections obtained by M. Roelands and the author in arXiv:2507.09526. To this end, we show that a unital operator system is completely order isomorphic to a C*-algebra if and only if each of its matrix spaces admits a compatible JB-algebra structure. As an application, we prove that for $n\ge 4$ the range of a unital n-positive projection on a unital real C*-algebra is unitally n-order isomorphic to a unital real C*-algebra, which is the analogue of a result proven for complex C*-algebras by Choi--Effros.

math.OA↗

arXiv2025

An order-theoretic characterization of JB-algebras

We give an order-theoretic characterization of the JB-algebras among the complete order unit spaces in terms of the existence of an order-anti-automorphism of the interior of the cone that is homogeneous of degree -1. More geometrically, we characterize JB-algebras as those complete order unit spaces for which the interior of the cone is a symmetric Banach--Finsler manifold under Thompson's metric. Furthermore, we show that two order unit spaces are isomorphic if there exists a gauge-reversing bijection between them, thus answering a question raised by Noll--Sch\"afer. These results have previously been established for finite-dimensional resp. reflexive order unit spaces by Walsh and Lemmens--R.--Wortel.

math.FA↗