Duality and o − O-structure in non reflexive Banach spaces

Authors

DOI:

https://doi.org/10.1478/AAPP.98S2A7

Keywords:

Duality, Distance formula

Abstract

Let E be a Banach space with a supremum type norm induced by a collection of functionals  ℒ ⊂ X* where X is a reflexive Banach space. Familiar spaces of this type are BMO, BV, C 0,α(0<α≤1), Lq,∾, for q>1. For most of these spaces E, the predual E* exists and can be defined by atomic decomposition of its elements. Another typical result, when it is possible to define a rich vanishing subspace E0 ⊂ E is the "two star theorem", namely (E0)*=E*. This fails for E=BV and E=C0,1=Lip.

Author Biographies

  • Luigi D'Onofrio, Università degli Studi di Napoli "Parthenope"
    Centro Direzionale Isola
  • Carlo Sbordone, Università degli Studi di Napoli Federico II
    Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
  • Roberta Schiattarella, Università degli Studi di Napoli Federico II
    Dipartimento di Matematica e Applicazioni "R. Caccioppoli"

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Published

2020-12-13

Issue

Vol 98, SUPPL NO 2 (2020): VA.PDE.ME.19

Section

Variational Analysis, PDEs and Mathematical Economics (Conference Proceedings)

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