An estimation of the Banach-Mazur distance between the space of convergent sequences and a concrete model of a space of affine continuous functions
DOI:
https://doi.org/10.12775/TMNA.2025.033Keywords
Banach-Mazur distance, space of convergent sequences, hyperplane, space of affine continuous functionsAbstract
In this paper $c$ denotes the space of convergent sequences endowed with the supremum norm and $\mathcal{W}$ is the hyperplane of $c$ defined by $\mathcal{W}=\Big\{ (x(i))\in c: \lim\limits_{i\to\infty}({x(1)+x(2)})/{2}\Big\}$. We pose the problem of determining the Banach-Mazur distance $d(c,\mathcal{W})$ and present a method to estimate such distance from below together with tight bounds for $d(\mathcal{W},c)$.References
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