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  • Publication
    The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
    (Elsevier, 2010-07) ;
    In 1976 Procesi and Schacher developed an Artin–Schreier type theory for central simple algebras with involution and conjectured that in such an algebra a totally positive element is always a sum of hermitian squares. In this paper elementary counterexamples to this conjecture are constructed and cases are studied where the conjecture does hold. Also, a Positivstellensatz is established for noncommutative polynomials, positive semidefinite on all tuples of matrices of a fixed size.
    Scopus© Citations 4  378