Calkin Images of Fourier Convolution Operators with Slowly Oscillating Symbols

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Abstract

Let be a Csubalgebra of L(formula presented) be the Banach algebra of slowly oscillating Fourier multipliers on a Banach function space X(ℝ). We show that the intersection of the Calkin image of the algebra generated by the operators of multiplication aI by functions a and the Calkin image of the algebra generated by the Fourier convolution operators W0(b) with symbols in (formula presented) coincides with the Calkin image of the algebra generated by the operators of multiplication by constants.

Original languageEnglish
Title of host publicationOperator Theory: Advances and Applications
EditorsM. A. Bastos, L. Castro, A. Y. Karlovich
Place of PublicationCham
PublisherBirkhäuser/Springer
Pages193-218
Number of pages26
ISBN (Electronic)978-3-030-51945-2
ISBN (Print)978-3-030-51944-5
DOIs
Publication statusPublished - 2021

Publication series

NameOperator Theory: Advances and Applications
PublisherBirkhäuser/Springer
Volume282
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Calkin algebra
  • Calkin image
  • Fourier convolution operator
  • Fourier multiplier
  • Multiplication operator
  • Slowly oscillating function

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