Invariant linear functionals on L(R+)

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Abstract

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
Volume481
Issue number1
DOIs
Publication statusPublished - 2020 Jan 1

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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