Invariant linear functionals on L(R+)

Ryoichi Kunisada

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1 Citation (Scopus)


We consider a continuous version of the classical notion of Banach limits, i.e., normalized positive linear functionals on L(R+) invariant under translations f(x)↦f(x+s) of L(R+) for every s≥0. We give one of its characterizations in terms of the invariance under the operation of a certain linear transformation on L(R+). We also deal with invariant linear functionals under dilations f(x)↦f(rx), r≥1 and give a similar characterization via the Hardy operator. Applications to summability methods are presented in the last section.

Original languageEnglish
Article number123452
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2020 Jan 1


  • Banach limits
  • Cesàro operator
  • Hardy operator
  • Invariant measures
  • Summability methods

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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