Noncommutative Positivstellensatze for pairs representation-vector

作者：Cimpric Jakob^*

来源：Positivity, 2011, 15(3): 481-495.

DOI：10.1007/s11117-010-0098-0

• Positive polynomials
• Real algebraic geometry
• Matrix polynomials
• Free algebras
• Algebras with involution

We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs (pi, upsilon) where pi is an unbounded *-representation of A on an inner product space which contains the vector upsilon. 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 A. Finally, we compare our results with their analogues in the usual (i.e. Schmudgen's) non-commutative real algebraic geometry where the points are unbounded *-representation of A.

• 出版日期2011-9