BIDUAL OCTAHEDRAL RENORMINGS AND STRONG REGULARITY IN BANACH SPACES
2019 ◽
pp. 1-17
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Keyword(s):
We prove that every separable Banach space containing an isomorphic copy of $\ell _{1}$ can be equivalently renormed so that the new bidual norm is octahedral. This answers, in the separable case, a question in Godefroy [Metric characterization of first Baire class linear forms and octahedral norms, Studia Math. 95 (1989), 1–15]. As a direct consequence, we obtain that every dual Banach space, with a separable predual and failing to be strongly regular, can be equivalently renormed with a dual norm to satisfy the strong diameter two property.
2010 ◽
Vol 83
(2)
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pp. 231-240
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Keyword(s):
2019 ◽
Vol 99
(03)
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pp. 467-472
Keyword(s):
1981 ◽
Vol 90
(1-2)
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pp. 63-70
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Keyword(s):
1971 ◽
Vol 12
(1)
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pp. 106-114
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1995 ◽
Vol 58
(2)
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pp. 222-231
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