# 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 $${\mathcal {A}}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Noncommutative Positivstellensätze for pairs representation-vector

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

/lp/springer_journal/noncommutative-positivstellens-tze-for-pairs-representation-vector-Qmwgh4mqvZ
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0098-0
Publisher site
See Article on Publisher Site

### Abstract

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 $${\mathcal {A}}$$ .

### Journal

PositivitySpringer Journals

Published: Oct 23, 2010

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### DeepDyve Freelancer ### DeepDyve Pro Price FREE$49/month

\$360/year
Save searches from