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  • Noncommutative partial convexity via ▫$\Gamma$▫-convexity
    Jury, Michael ...
    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 ▫$\mathcal{K}$▫ is called ▫$\Gamma$▫-convex if for all ▫$ X\in \mathcal{K}$▫ and isometries ▫$V$▫ satisfying ▫$\,V^*\Gamma(X)V = \Gamma(V^*XV)$▫, we have ▫$V^*XV \in\mathcal{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$▫.
    Vir: The Journal of geometric analysis. - ISSN 1050-6926 (Vol. 31, iss. 3, March 2021, str. 3137-3160)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 105932035

    Povezava(-e):

    https://link.springer.com/article/10.1007/s12220-020-00387-1
    DOI

vir: The Journal of geometric analysis. - ISSN 1050-6926 (Vol. 31, iss. 3, March 2021, str. 3137-3160)
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