Simple archimedean dimension groups
We answer a question of Goodearl, by constructing for every metrizable Choquet simplex, a dimension group that is simple and archimedean and whose trace space is the desired Choquet simplex.
math.RA↗
arXiv subjects
David Handelman
Publications and source records attributed to David Handelman.
Real dimension groups
We show the characterization analogous to dimension groups of partially ordered real vector spaces with interpolation works, but sequential direct limits of simplicial vector spaces only under strong assumptions. We also provide and generalize a proof of a result of Fuchs asserting that the real polynomial algebra with pointwise ordering coming from an interval satisfies Riesz interpolation
math.RA↗
Arguments of zeros of highly log concave polynomials
For a real polynomial $p = \sum_{i=0}^{n} c_ix^i$ with no negative coefficients and $n\geq 6$, let $β(p) = \inf_{i=1}^{n-1} c_i^2/c_{i+1}c_{i-1}$ (so $β(p) \geq 1$ entails that $p$ is log concave). If $β(p) > 1.45...$, then all roots of $p$ are in the left half plane, and moreover, there is a function $β_0 (θ)$ (for $π/2 \leq θ\leq π$) \st $β\geq β_0(θ)$ entails all roots of $p$ have arguments in the sector $| \arg z| \geq θ$ with the smallest possible $θ$; we determine exactly what this function (and its inverse) is (it turns out to be piecewise smooth, and quite tractible). This is a one-parameter extension of Kurtz's theorem (which asserts that $β\geq 4$ entails all roots are real). We also prove a version of Kurtz's theorem with real (not necessarily nonnegative) coefficients.
math.CA↗
In praise of order units
We show that the ordered rings naturally associated to compact convex polyhedra with interior satisfy a positivity property known as order unit cancellation, and obtain other general positivity results as well.
math.AG↗