On the diameter of the Banach-Mazur set

Title:

On the diameter of the Banach-Mazur set

Creator:

Godefroy, Gilles

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3157c9b4-c3ee-4dbb-98b4-3c930a0f7724
uuid:3157c9b4-c3ee-4dbb-98b4-3c930a0f7724

Subject:

Banach-Mazur diameter, elastic Banach spaces, and Martin's Maximum axiom

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

95-100

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:1

Harvested from:

CDK

Metadata only:

false