Noncommutative Partial Convexity Via $$\Gamma $$-Convexity
Noncommutative Partial Convexity Via $$\Gamma $$-Convexity
复制标题
通过 $$Gamma $$-凸性实现非交换部分凸性
DOI：
10.1007/s12220-020-00387-1
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Pascoe, James Eldred
中科院分区：
文献类型：
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作者：
Jury, Michael;Klep, Igor;Mancuso, Mark E.;McCullough, Scott;Pascoe, James Eldred
受经典的部分凸性，双凸性和双线性矩阵不等式的概念的启发，我们研究了自由集的理论，自由集是由（低次）非交换矩阵多项式的约束条件。给定一个对称多项式元组，一个自由集称为-凸集，如果对所有的和等距线V满足，我们建立了-凸集的Effros-Winkler-Hahn-Banach分离定理;它们在和变量x的坐标中用线性束描绘。
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, a free setis called-convex if for alland isometriesVsatisfying, we haveWe establish an Effros–Winkler Hahn–Banach separation theorem for-convex sets; they are delineated by linear pencils in the coordinates ofand the variablesx.