论文标题
SU（2）中的循环和分解，II
Loops in SU(2) and Factorization, II
论文作者
论文摘要
在本文的前传中，我们证明，对于$ su（2，\ mathbb c）$值的循环具有关键的光滑度（在$ l^2 $ sobolev sensic中的衍生物中的一半），以下陈述是等效的：（1）toeplitz and toeplitz and toeplitz operator a toeplitz operatian coptian toeplitz operian with loop a intorian toriand probiriand promiantian toriand in witian no probiriand（2）（2）（2）（2）（2）（2） （3）循环具有独特的根部亚组分解。这取决于某些plancherel风格的公式，以确保Toeplitz运营商的决定因素。该报告的要点是概述了该结果对消失的平均振荡循环的概括，并讨论了一些后果。这种概括取决于Toeplitz运算符的操作者理论分解（不仅是其决定因素）。
In the prequel to this paper, we proved that for a $SU(2,\mathbb C)$ valued loop having the critical degree of smoothness (one half of a derivative in the $L^2$ Sobolev sense), the following statements are equivalent: (1) the Toeplitz and shifted Toeplitz operators associated to the loop are invertible, (2) the loop has a unique triangular factorization, and (3) the loop has a unique root subgroup factorization. This hinges on some Plancherel-esque formulas for determinants of Toeplitz operators. The main point of this report is is to outline a generalization of this result to loops of vanishing mean oscillation, and to discuss some consequences. This generalization hinges on an operator-theoretic factorization of the Toeplitz operators (not simply their determinants).
