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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}
}

. 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… Expand

For a locally compact Hausdorff spaceK and a Banach space X we denote by C0(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a… Expand

We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Gordon,… Expand

Let $C_0(K, X)$ denote the space of all continuous $X$-valued functions defined on the locally compact Hausdorff space $K$ which vanish at infinity, provided with the supremum norm. If $X$ is the… Expand

Abstract Let $X$ be a Banach space and $\xi$ an ordinal number. We study some isomorphic classifications of the Banach spaces $X^\xi$ of the continuous $X$-valued functions defined in the interval of… Expand

IfX, Y are compact countable metric spaces such thatY contains no subset homeomorphic toX, then for any isomorphismΦ ofC(X) intoC(Y), ‖ φ ‖ ‖ φ−1 ‖≧3. This result and some variants of it are… Expand