116 citations · 1.1k across the 72 of their papers we have counts for
13 papers · 1 filter
Duality, extreme points and hulls for noncommutative partial convexity
Igor Klep, Scott McCullough, Tea Štrekelj
This article studies generalizations of (matrix) convexity, including partial convexity and biconvexity, under the umbrella of -convexity. Here is a tuple of free symmetric…
Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
Igor Klep, Claus Scheiderer, Jurij Volčič
A noncommutative (nc) polynomial is called (globally) trace-positive if its evaluation at any tuple of operators in a tracial von Neumann algebra has nonnegative trace. Such polyno…
Extreme points of matrix convex sets, free spectrahedra and dilation theory
Eric Evert, J. William Helton, Igor Klep +1
For matrix convex sets a unified geometric interpretation of notions of extreme points and of Arveson boundary points is given. These notions include, in increasing order of streng…
Circular Free Spectrahedra
Eric Evert, J. William Helton, Igor Klep +1
This paper considers matrix convex sets invariant under several types of rotations. It is known that matrix convex sets that are free semialgebraic are solution sets of Linear Matr…
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…
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…