Positivstellensätze for Algebras of Matrices

Details Positivstellensätze for Algebras of Matrices Positivstellensätze for Algebras of Matrices

2010-04-09

arxiv.org/abs/1004.1529v2

Mathematics

Algebraic Geometry

28 pages

Scientific paper

The paper is concerned with various types of noncommutative Positivstellens\"atze for the matrix algebra $M_n(\cA)$, where $\cA$ is an algebra of operators acting on a unitary space, a path algebra, a cyclic algebra or a formally real field. Some new types of Positivstellens\"atze are proposed and proved, it is shown by examples that they occur. There are a number of results stating that a type of Positivstellensatz is valid for $M_n(\cA)$ provided that it holds for $\cA$.

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