A C-algebra of Singular Integral Operators with Shifts and Piecewise Quasicontinuous Coefficients

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

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Abstract

The C-algebra B of bounded linear operators on the space L2}T, which is generated by all multiplication operators by piecewise quasicontinuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of a group G of orientation-preserving diffeomorphisms of T onto itself that have the same finite set of fixed points for all (Formula presented), is studied. A Fredholm symbol calculus for the C-algebra B and a Fredholm criterion for the operators (Formula presented) are established by using spectral measures and the local-trajectory method for studying C-algebras associated with C-dynamical systems.

Original languageEnglish
Title of host publicationOperator Theory: Advances and Applications
PublisherSpringer International Publishing Switzerland
Pages25-64
Number of pages40
DOIs
Publication statusPublished - 1 Jan 2018

Publication series

NameOperator Theory: Advances and Applications
PublisherSpringer International Publishing Switzerland
Volume267
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Amenable group
  • C-algebra
  • Fredholmness
  • Local-trajectory method
  • Piecewise quasicontinuous function
  • Representation of a C-algebra
  • Singular integral operator with shifts
  • Spectral measure
  • Symbol calculus

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