We introduce the concept of *-mapping as a selection of the duality mapping. We prove that the *-mappings are more general than the support mappings and provide a simple proof of the characterisation of smoothness by the norm to weak-star continuity of the *-mappings. As a consequence, we provide a characterisation of Hilbert spaces in terms of *-mappings and show that a Banach space has the Schur property if and only if it has the Dunford-Pettis property and there exists a *-mapping that is sequentially w – w continuous at 0. This last fact leads to the existence of smooth Banach spaces on which the duality mapping is not sequentially w – w continuous at 0.

Selectors of the duality mapping.

PUGLISI, DANIELE
2016

Abstract

We introduce the concept of *-mapping as a selection of the duality mapping. We prove that the *-mappings are more general than the support mappings and provide a simple proof of the characterisation of smoothness by the norm to weak-star continuity of the *-mappings. As a consequence, we provide a characterisation of Hilbert spaces in terms of *-mappings and show that a Banach space has the Schur property if and only if it has the Dunford-Pettis property and there exists a *-mapping that is sequentially w – w continuous at 0. This last fact leads to the existence of smooth Banach spaces on which the duality mapping is not sequentially w – w continuous at 0.
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: http://hdl.handle.net/20.500.11769/253134
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact