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Keywords:
Banach-Mazur diameter; elastic Banach spaces; Martin's Maximum axiom
Banach-Mazur diameter; elastic Banach spaces; Martin's Maximum axiom
Summary:
On every subspace of $l_{\infty }(\mathbb N)$ which contains an uncountable $\omega $-independent set, we construct equivalent norms whose Banach-Mazur distance is as large as required. Under Martin's Maximum Axiom (MM), it follows that the Banach-Mazur diameter of the set of equivalent norms on every infinite-dimensional subspace of $l_{\infty }(\mathbb N)$ is infinite. This provides a partial answer to a question asked by Johnson and Odell.
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