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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