Convolution Operators on Banach Lattices with Shift-Invariant Norms

Nazar Miheisi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let G be a locally compact abelian group and let μ be a complex valued regular Borel measure on G. In this paper we consider a generalisation of a class of Banach lattices introduced in Johansson (Syst Control Lett 57:105-111, 2008). We use Laplace transform methods to show that the norm of a convolution operator with symbol μ on such a space is bounded below by the L norm of the Fourier-Stieltjes transform of μ. We also show that for any Banach lattice of locally integrable functions on G with a shift-invariant norm, the norm of a convolution operator with symbol μ is bounded above by the total variation of μ.

Original languageEnglish
Pages (from-to)287-299
Number of pages13
JournalINTEGRAL EQUATIONS AND OPERATOR THEORY
Volume68
Issue number2
DOIs
Publication statusPublished - 19 Jul 2010

Keywords

  • Convolution operator
  • laplace transform
  • shift-invariant norm

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