Konrad Schmüdgen
Positivstellens\"atze for Algebras of Matrices.
Mon, 04/12/2010 - 15:01 — SomNambulAuthors: Yurii Savchuk, Konrad Schmüdgen
Subjects: Algebraic Geometry
AbstractThe 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 $\cA$.A noncommutative version of the Fej\'er-Riesz theorem.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Yurii Savchuk, Konrad Schmüdgen
Subjects: Operator Algebras
AbstractLet $\cX$ be the unital *-algebra generated by the unilateral shift operator.
It is shown that for any nonnegative operator $X\in \cX$ there is an element
$Y\in \cX$ such that $X=Y^*Y$.A noncommutative version of the Fej\'er-Riesz theorem.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Yurii Savchuk, Konrad Schmüdgen
Subjects: Operator Algebras
AbstractLet $\cX$ be the unital *-algebra generated by the unilateral shift operator.
It is shown that for any nonnegative operator $X\in \cX$ there is an element
$Y\in \cX$ such that $X=Y^*Y$.
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