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On a Question by Markus Seidel

  • Davor Dragičević
  • Guida Preto
  • Pedro A. Santos
  • Marcin Szamotulski
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 242)

Abstract

We give necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication and the convolution operators with piecewise continuous generating functions on \(L^{p}(\mathbb{R}),\,1\,<\,p\,<\,\infty\) using a variation from the standard technique. We prove that it is possible to arrive to this result using only strong-limit homomorphism and with considerable simplification of the standard identification procedure for the local algebras.

Keywords

Finite section method Stability Banach algebra local principle 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Davor Dragičević
    • 1
    • 2
  • Guida Preto
    • 3
  • Pedro A. Santos
    • 4
  • Marcin Szamotulski
    • 5
    • 6
  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal
  2. 2.Department of MathematicsUniversity of RijekaRijekaCroatia
  3. 3.Departamento de MathemáticaInstituto Superior Técnico Universidade Técnica de LisboaLisboaPortugal
  4. 4.Centro de Análise Funcional e Aplicações Departamento de MatemáticaInstituto Superior Técnico Universidade Técnica de LisboaLisboaPortugal
  5. 5.Center for Mathematical Analysis, Geometry, and Dynamical Systems Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal
  6. 6.National Institute of TelecommunicationsWarsawPoland

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