In his celebrated paper in 1976, A. Connes casually remarked that any finite von Neumann
algebra ought to be embedded into an ultraproduct of matrix algebras, which is now known …

This paper introduces state polynomials, ie, polynomials in noncommuting variables and
formal states of their products. A state analog of Artin's solution to Hilbert's 17th problem is …

Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathematics. The …

In this note we address various algorithmic problems that arise in the computation of the
operator norm in unitary representations of a group on a Hilbert space. We show that the …

Let M be an archimedean quadratic module of real t× t matrix polynomials in n variables,
and let S⊆ ℝn be the set of all points where each element of M is positive semidefinite. Our …

It is well known that an element of the algebra of noncommutative*-polynomials is positive in
all*-representations if and only if it is a sum of squares. This provides an effective way to …

In this paper we develop a number of results and notions concerning Positivstellensätze for
semirings (preprimes) of commutative unital real algebras. First we reduce the Archimedean …

Mathematische Annalen Page 1 DOI: 10.1007/s00208-004-0604-4 Math. Ann. 331, 779–794
(2005) Mathematische Annalen A strict Positivstellensatz for the Weyl algebra Konrad …

Haviland's theorem states that given a closed subset K in Rn, each functional L: R [x¯]→ R
positive on Pos (K)≔{p∈ R [x¯]| p| K≥ 0} admits an integral representation by a positive …

Mathematische Zeitschrift Page 1 Math. Z. (2007) 255:579–596 DOI 10.1007/s00209-006-0032-0
Mathematische Zeitschrift Strong majorization in a free ∗-algebra J. William Helton · Scott …