Positivstellensätze for Algebras of Matrices

2010/04/09 by Savchuk, Yurii, Schmüdgen, Konrad
#14P99 #15B33 #15B48 #Algebraic Geometry (math.AG) #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1004.1529

Abstract

The paper is concerned with various types of noncommutative Positivstellensätze 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 Positivstellensätze 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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