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On convoluters on $L^p$-spaces

Volume 245 / 2019

Matthew Daws, Nico Spronk Studia Mathematica 245 (2019), 15-31 MSC: Primary 43A15; Secondary 22D12, 47L10. DOI: 10.4064/sm170601-24-11 Published online: 29 June 2018

Abstract

We prove two theorems about convolution operators on $L^p(G)$ for a locally compact group $G$. First, if $G$ has the approximation property, then the algebra of convoluters is the algebra of pseudo-measures. Second, the bicommutant of the algebra of pseudo-measures is the algebra of convoluters.

Authors

  • Matthew DawsJeremiah Horrocks Institute
    University of Central Lancashire
    Preston, PR1 2HE, United Kingdom
    e-mail
  • Nico SpronkDepartment of Pure Mathematics University of Waterloo
    Waterloo, Ontario, N2L 3G1, Canada
    e-mail

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