Noncommutative Positivstellens\"atze for pairs representation-vector
Algebraic Geometry
2013-07-09 v2 Functional Analysis
Abstract
We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space which contains the vector v. We first consider the *-algebras of matrices of usual and free multivariate polynomials with their natural subsets of points. If all points are allowed then we can obtain results for general A. Finally, we compare our results with their analogues in the usual (i.e. Schm\"udgen's) non-commutative real algebraic geometry where the points are unbounded *-representation of A.
Cite
@article{arxiv.1011.4927,
title = {Noncommutative Positivstellens\"atze for pairs representation-vector},
author = {Jaka Cimpric},
journal= {arXiv preprint arXiv:1011.4927},
year = {2013}
}
Comments
16 pages. The final version