Noncommutative Positivstellensätze for pairs representation-vector

Noncommutative Positivstellensätze for pairs representation-vector 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 results with their analogues in the usual (i.e. Schmüdgen’s) non-commutative real algebraic geometry where the points are unbounded *-representation of $${\mathcal {A}}$$ . Positivity Springer Journals

Noncommutative Positivstellensätze for pairs representation-vector

Positivity , Volume 15 (3) – Oct 23, 2010

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SP Birkhäuser Verlag Basel
Copyright © 2010 by Springer Basel AG
Mathematics; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Operator Theory; Fourier Analysis
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