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EnglishWe present a Lindenstrauss space with an extreme point that does not contain a subspace linearly isometric to c. This example disproves a re- sult stated by Zippin in a paper published in 1969 and it shows that some classical characterizations of polyhedral Lindenstrauss spaces, based on Zippin’s result, are false, whereas some others remain unproven; then we provide a correct proof for those characterizations. Finally, we also disprove a characterization of polyhedral Lindenstrauss spaces given by Lazar, in terms of the compact norm-preserving extension of compact op- erators, and we give an equivalent condition for a Banach space X to satisfy this property.
| Autori: | |
| Titolo: | Rethinking polyhedrality for Lindenstrauss spaces |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s11856-016-1412-8 |
| URL: | http://link.springer.com/article/10.1007%2Fs11856-016-1412-8 |
| Data di pubblicazione: | 2016 |
| Abstract: | We present a Lindenstrauss space with an extreme point that does not contain a subspace linearly isometric to c. This example disproves a re- sult stated by Zippin in a paper published in 1969 and it shows that some classical characterizations of polyhedral Lindenstrauss spaces, based on Zippin’s result, are false, whereas some others remain unproven; then we provide a correct proof for those characterizations. Finally, we also disprove a characterization of polyhedral Lindenstrauss spaces given by Lazar, in terms of the compact norm-preserving extension of compact op- erators, and we give an equivalent condition for a Banach space X to satisfy this property. |
| Lingua: | Inglese |
| Rivista: | |
| Citazione: | Casini, E., Miglierina, E., Piasecki, L., Veselý, L., Rethinking polyhedrality for Lindenstrauss spaces, <<ISRAEL JOURNAL OF MATHEMATICS>>, 2016; 216 (1): 355-369. [doi:10.1007/s11856-016-1412-8] [http://hdl.handle.net/10807/91182] |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
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