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EnglishWe 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.
| Titolo: | Selectors of the duality mapping. |
| Autori interni: | |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Handle: | http://hdl.handle.net/20.500.11769/253134 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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