In the prequel to this paper, we proved that for a SU(2, C) valued loop having the critical degree of smoothness (one half of a derivative in the L2 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).
|Original language||English (US)|
|State||Published - Sep 29 2020|
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