116 citations · 1.1k across the 72 of their papers we have counts for
4 papers · 1 filter
Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
J. William Helton, Igor Klep, Scott A. McCullough +1
An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V from H to K such that C=V^*TV. A main result of this paper is, for a posi…
On trace-convex noncommutative polynomials
Igor Klep, Scott A. McCullough, Christopher S. Nelson
To each real continuous function f there is an associated trace function on real symmetric matrices Tr f. The classical Klein lemma states that f is convex if and only if Tr f is c…
Free function theory through matrix invariants
Igor Klep, Špela Špenko
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommut…
The Tracial Hahn-Banach Theorem, Polar Duals, Matrix Convex Sets, and Projections of Free Spectrahedra
J. William Helton, Igor Klep, Scott McCullough
This article investigates matrix convex sets and introduces their tracial analogs which we call contractively tracial convex sets. In both contexts completely positive (cp) maps pl…