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arXiv · 2009.14267

Loops in SU(2) and Factorization, II

Estelle Basor·Doug Pickrell
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Abstract

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).

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Estelle Basor, Doug Pickrell. 2020-09-29. Loops in SU(2) and Factorization, II. https://arxiv.org/abs/2009.14267

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