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Positivstellens\"atze for Algebras of Matrices

Algebraic Geometry 2010-08-09 v2 Operator Algebras Rings and Algebras

Abstract

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

Keywords

Cite

@article{arxiv.1004.1529,
  title  = {Positivstellens\"atze for Algebras of Matrices},
  author = {Yurii Savchuk and Konrad Schmüdgen},
  journal= {arXiv preprint arXiv:1004.1529},
  year   = {2010}
}

Comments

28 pages