## Abstract

We prove that every separable polyhedral Banach space X is isomorphic to a

polyhedral Banach space Y such that, the set ext BY ∗ cannot be covered by a sequence of

balls B(yi, ²i) with 0 < ²i < 1 and ²i → 0. In particular ext BY ∗ cannot be covered by

a sequence of norm compact sets. This generalizes a result from [7] where an equivalent

polyhedral norm |||·||| on c0 was constructed such that ext B(c0,|||·|||)∗ is uncountable but

can be covered by a sequence of norm compact sets.

polyhedral Banach space Y such that, the set ext BY ∗ cannot be covered by a sequence of

balls B(yi, ²i) with 0 < ²i < 1 and ²i → 0. In particular ext BY ∗ cannot be covered by

a sequence of norm compact sets. This generalizes a result from [7] where an equivalent

polyhedral norm |||·||| on c0 was constructed such that ext B(c0,|||·|||)∗ is uncountable but

can be covered by a sequence of norm compact sets.

Original language | English |
---|---|

Pages (from-to) | 243-249 |

Journal | Extracta Mathematicae |

Volume | 24 |

Issue number | 3 |

State | Published - Feb 2009 |

Externally published | Yes |

## Keywords

- Mathematics