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The Procesi–Schacher conjecture for algebras with involution
Procesi–Schacher conjecture. Every totally $s$ -positive element of $A$ is a sum of hermitian squares. Equivalently, the trace of a hermitian square is always a sum of hermitian squ…
Conjectureopenalgebras-with-involution hilberts-seventeenth-problem quadratic-formsarXiv posted 2 days ago

The Procesi–Schacher conjecture for algebras with involution