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, C0,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.

Duality and o-O structure in non reflexive banach spaces

D'Onofrio L.;
2020

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, C0,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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/100437
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact