How many miles from $L_\infty$ to $\ell_\infty$?
Maciej Korpalski, Grzegorz Plebanek
TL;DR
This paper investigates the Banach-Mazur distance between the classical Banach spaces $L_[0,1]$ and ll_$, providing bounds on how far apart they are in the Banach-Mazur sense.
Contribution
It establishes new lower and upper bounds for the Banach-Mazur distance between $L_[0,1]$ and ll_$, advancing understanding of their geometric relationship.
Findings
Derived bounds for the Banach-Mazur distance between the spaces.
Showed that the spaces are not isometric but quantified their distance.
Provided insights into the geometric structure of classical Banach spaces.
Abstract
The classical Banach spaces and are isomorphic. We present here some lower and upper bounds for their Banach-Mazur distance.
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