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 |
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Pages (from-to) | 243-249 |
Journal | Extracta Mathematicae |
Volume | 24 |
Issue number | 3 |
State | Published - Feb 2009 |
Externally published | Yes |
Keywords
- Mathematics