@inbook{646b030f057d4ecf961ac44c1cf9b9a4,
title = "Loops in SU(2) and Factorization, II",
abstract = "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. These equivalences hinge on factorization formulas for determinants of Toeplitz operators. The main point of this sequel is to discuss generalizations to measurable loops, in particular loops of vanishing mean oscillation. The VMO generalization hinges on an operator-theoretic factorization for Toeplitz operators, in lieu of factorization for determinants.",
keywords = "Factorization, Hankel, Toeplitz, Vanishing mean oscillation",
author = "Estelle Basor and Doug Pickrell",
note = "Funding Information: Acknowledgments The first author was supported in part by the American Institute of Mathematics and the NSF grant DMS-1929334. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2022",
doi = "https://doi.org/10.1007/978-3-031-13851-5_9",
language = "English (US)",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "117--149",
booktitle = "Operator Theory",
address = "Germany",
}