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arXiv · 2511.03435

Bounds for Banach-Mazur distances between some $C(K)$-spaces

Maciej Korpalski·Grzegorz Plebanek
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Abstract

We present several results providing lower bounds for the Banach-Mazur distance \[d_{BM}(C(K), C(L))\] between Banach spaces of continuous functions on compact spaces. The main focus is on the case where $C(L)$ represents the classical Banach space $c$ of convergent sequences. In particular, we obtain generalizations and refinements of recent results from \cite{GP24} and \cite{MP25}. Currently, it seems that one of the most interesting questions is when $K = [0, \omega]$ is a convergent sequence with a limit and $L = [0,\omega]\times 3$ consists of three convergent sequences. In this case, we obtain \[3.53125 \leq d_{BM}(C([0,\omega]\times 3),C[0,\omega]) \leq 3.87513\]

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Maciej Korpalski, Grzegorz Plebanek. 2025-11-05. Bounds for Banach-Mazur distances between some $C(K)$-spaces. https://arxiv.org/abs/2511.03435

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