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Orlicz spaces with a oO type structure

  • Francesca AngrisaniEmail author
  • Giacomo Ascione
  • Gianluigi Manzo
Article
  • 15 Downloads

Abstract

We study non reflexive Orlicz spaces \(L^\varPsi \) and their Morse subspace \(M^\varPsi \), i.e. the closure of \(L^\infty \) in \(M^\varPsi \) to determine when \((M^\varPsi ,L^\varPsi )\) can be described as having an oO type structure with respect to an equivalent norm on \(L^\varPsi \). Examples of classes of Young functions for which the answer is affirmative are provided, but also examples are given to show that this is not possible for all non-reflexive Orlicz spaces. An equivalent expression of the distance in \(L^\varPsi \) to \(M^\varPsi \), induced by the new norm, is also provided.

Keywords

Orlicz space M-ideal Rearrangement Distance 

Mathematics Subject Classification

46E30 

Notes

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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”Università degli Studi di Napoli Federico IINaplesItaly

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