Positivstellens\"atze for Algebras of Matrices
Abstract
The paper is concerned with various types of noncommutative Positivstellens\"atze for the matrix algebra Mn(), where 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 Mn() provided that it holds for .
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