Banach–Mazur radius of nonseparable infinite-dimensional Banach spaces

Determine whether the Banach–Mazur radius \(R_{BM}(X)\) is infinite for every nonseparable infinite-dimensional Banach space \(X\).

Background

The paper recalls a longstanding infinite-dimensional question concerning Banach–Mazur radii. Although Johnson and Odell proved that $R_{BM}(X)=\infty$ for every infinite-dimensional Banach space in the relevant separable setting, the authors state that the corresponding assertion for all nonseparable Banach spaces is still unresolved. This question is separate from the finite-dimensional problem treated in the main theorem but is explicitly included as an open problem in the paper.