Loops in SU(2) and Factorization, II

Estelle Basor, Doug Pickrell

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages33
StatePublished - 2022

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


  • Factorization
  • Hankel
  • Toeplitz
  • Vanishing mean oscillation

ASJC Scopus subject areas

  • Analysis


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