A Hermitian analogue of the Bröcker-Prestel theorem

The Bröcker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the Henselizations and isotropy over the real closures of that field. A Hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of Pythagorean index at most two, and algebras over SAP and ED fields.