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Journal article
Noncommutative Partial Convexity Via Gamma-Convexity
The Journal of geometric analysis, v 31(3), pp 3137-3160
01 Mar 2021
Abstract
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 K is called Gamma-convex if for all X is an element of K and isometries V satisfying V*Gamma(X)V=Gamma(V*XV), we have V*XV is an element of K. 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 Jury - University of FloridaIgor Klep - University of LjubljanaMark E. Mancuso - Washington University in St. LouisScott McCullough - University of FloridaJames Eldred Pascoe - University of Florida
- Publication Details
- The Journal of geometric analysis, v 31(3), pp 3137-3160
- Publisher
- Springer Nature
- Number of pages
- 24
- Grant note
- DMS 1606260 / NSF MSPRF; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) DMS-1361501; DMS-1764231; DMS-1900364; DMS-1565243 / NSF; National Science Foundation (NSF) J1-8132; N1-0057; P1-0222 / Slovenian Research Agency; Slovenian Research Agency - Slovenia Marsden Fund Council of the Royal Society of New Zealand; Royal Society of New Zealand; Marsden Fund (NZ)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000518345600001
- Scopus ID
- 2-s2.0-85081691243
- Other Identifier
- 991021879787004721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics