A C*-algebra of singular integral operators with shifts similar to affine mappings

M. Amélia Bastos, Cláudio A. Fernandes, Yuri I. Karlovich

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Citations (Scopus)

Abstract

Representations on Hilbert spaces for the nonlocal C*-algebra B of singular integral operators with piecewise slowly oscillating coefficients, which is extended by the unitary shift operators Ug associated with the solvable discrete group G of diffeomorphisms g : T → T that are similar to affine mappings on the real line, are constructed. Such shifts may change or preserve the orientation on T and have both common fixed points for all g Є G and distinct fixed points for different shifts. Using the theory developed for C*-algebras of singular integral operators with shifts preserving the orientation of a contour, a Fredholm symbol calculus for the C*-algebra B is constructed and a Fredholm criterion for the operators B Є B is established.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing Switzerland
Pages53-79
Number of pages27
Publication statusPublished - 2014

Publication series

NameOperator Theory: Advances and Applications
Volume242
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Affine shifts
  • Amenable group
  • C*-algebra
  • Fredholm-ness
  • Lifting theorem
  • Local-trajectory method
  • Piecewise slowly oscillating function
  • Representation
  • Singular integral operator with shifts
  • Spectral measure
  • Symbol calculus

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