Open Research Index

ehrlich-b/sequential-products-lean

Bryan Ehrlich

Palomar Registrypalomar/PALOMAR-2026-08-21-000001Aug 21, 2026math.OAscore 0

A sequential product on the effects of an order-unit space is a binary operation a & b, read "first test a, then test b with the state updated by the first test", satisfying the seven axioms S1-S7 of van de Wetering (arXiv:1803.11139, Definition 2). This development registers two classification theorems for such products on the Hermitian matrix algebras. On H_N(R), the Hermitian N x N real matrices with N >= 1, every sequential product is the Lueders product sqrt(a) b sqrt(a): there is no free parameter. On H_N(C) with N >= 3, every sequential product has the twist normal form a^(1/2+it) b…

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