# Noncommutative Positivstellensätze for pairs representation-vector

@article{Cimpric2010NoncommutativePF,
title={Noncommutative Positivstellens{\"a}tze for pairs representation-vector},
author={J. Cimpric},
journal={Positivity},
year={2010},
volume={15},
pages={481-495}
}
• J. Cimpric
• Published 22 November 2010
• Mathematics
• Positivity
We study non-commutative real algebraic geometry for a unital associative *-algebra $${\mathcal {A}}$$ viewing the points as pairs (π, v) where π is an unbounded *-representation of $${\mathcal A}$$ on an inner product space which contains the vector v. We first consider the *-algebras of matrices of usual and free real multivariate polynomials with their natural subsets of points. If all points are allowed then we can obtain results for general $${\mathcal {A}}$$. Finally, we compare our… Expand
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