• Corpus ID: 249889172

# Isomorphisms of $\mathcal{C}(K, E)$ spaces and height of $K$

@inproceedings{Rondovs2022IsomorphismsO,
title={Isomorphisms of \$\mathcal\{C\}(K, E)\$ spaces and height of \$K\$},
author={Jakub Rondovs and Jacopo Somaglia},
year={2022}
}
• Published 18 June 2022
• Mathematics
. Let K 1 , K 2 be compact Hausdorﬀ spaces and E 1 ,E 2 be Banach spaces not containing a copy of c 0 . We establish lower estimates of the Banach- Mazur distance between the spaces of continuous functions C ( K 1 ,E 1 ) and C ( K 2 ,E 2 ) based on the ordinals ht ( K 1 ), ht ( K 2 ), which are new even for the case of spaces of real valued functions on ordinal intervals. As a corollary we deduce that C ( K 1 ,E 1 ) and C ( K 2 ,E 2 ) are not isomorphic if ht ( K 1 ) is substan-tially diﬀerent…

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