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arXiv · 1511.06330

Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher

Vincent Astier·Thomas Unger
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Abstract

Using the theory of signatures of hermitian forms over algebras with involution, developed by us in earlier work, we introduce a notion of positivity for symmetric elements and prove a noncommutative analogue of Artin's solution to Hilbert's 17th problem, characterizing totally positive elements in terms of weighted sums of hermitian squares. As a consequence we obtain an earlier result of Procesi and Schacher and give a complete answer to their question about representation of elements as sums of hermitian squares.

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Vincent Astier, Thomas Unger. 2015-11-19. Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher. https://arxiv.org/abs/1511.06330

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