1. On the diameter of the Banach-Mazur set
- Creator:
- Godefroy, Gilles
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Banach-Mazur diameter, elastic Banach spaces, and Martin's Maximum axiom
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public