论文标题
haagerup限制为Quaternionic Grothendieck不平等
Haagerup bound for quaternionic Grothendieck inequality
论文作者
论文摘要
我们在这里介绍了季节偏斜领域的几个版本的Grothendieck不平等：第一个是矩形矩阵的标准Grothendieck不平等，而自相关矩阵的另外两个不平等现象，正如最近在最近一篇论文中的第一和最后一位作者所介绍的那样。我们给出了``conic grothendieck不平等''的几个结果：作为Nesterov $π/2 $ -Theorem，对应于阳性半金属矩阵的锥； Goemans - 意愿不平等，与加权拉普拉斯人的锥相对应；对角矩阵。本文最具挑战性的技术部分是证明了Haagerup类似物的证明，导致超几何函数的倒数$ x {} _2f_1（\ frac {1} {2} {2} {2}，\ frac {1} {2} {2} {2} {2}; 3; x^2）
We present here several versions of the Grothendieck inequality over the skew field of quaternions: The first one is the standard Grothendieck inequality for rectangular matrices, and two additional inequalities for self-adjoint matrices, as introduced by the first and the last authors in a recent paper. We give several results on ``conic Grothendieck inequality'': as Nesterov $π/2$-Theorem, which corresponds to the cones of positive semidefinite matrices; the Goemans--Williamson inequality, which corresponds to the cones of weighted Laplacians; the diagonally dominant matrices. The most challenging technical part of this paper is the proof of the analog of Haagerup result that the inverse of the hypergeometric function $x {}_2F_1(\frac{1}{2}, \frac{1}{2}; 3; x^2)$ has first positive Taylor coefficient and all other Taylor coefficients are nonpositive.
