Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895934 | Journal of Algebra | 2018 | 25 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Vincent Astier, Thomas Unger,