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.

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]

Rethinking polyhedrality for Lindenstrauss spaces

Miglierina, Enrico;Piasecki, Lukasz;
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.
eng
http://link.springer.com/article/10.1007%2Fs11856-016-1412-8
Casini, E., Miglierina, E., Piasecki, L., Veselý, L., Rethinking polyhedrality for Lindenstrauss spaces, <>, 2016; 216 (1): 355-369. [doi:10.1007/s11856-016-1412-8] [http://hdl.handle.net/10807/91182]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/91182
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