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Preprint
Noncommutative partial convexity via $\Gamma$-convexity
16 Aug 2019
Abstract
J. Geom. Anal. 31 (2021) 3137--3160 Motivated by classical notions of partial convexity, biconvexity, and
bilinear matrix inequalities, we investigate the theory of free sets that are
defined by (low degree) noncommutative matrix polynomials with constrained
terms. Given a tuple of symmetric polynomials $\Gamma$, a free set is called
$\Gamma$-convex if it closed under isometric conjugation by isometries
intertwining $\Gamma$. We establish an Effros-Winkler Hahn-Banach separation
theorem for $\Gamma$-convex sets; they are delineated by linear pencils in the
coordinates of $\Gamma$ and the variables $x$.
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Details
- Title
- Noncommutative partial convexity via $\Gamma$-convexity
- Creators
- Michael JuryIgor KlepMark E MancusoScott McCulloughJames Eldred Pascoe
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021879756304721