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Proceedings of the Edinburgh Mathematical Society
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An example regarding Kalton's paper ‘isomorphisms between spaces of vector-valued continuous functions’

An example regarding Kalton's paper ``Isomorphisms between spaces of vector-valued continuous functions''
Authors: Cabello Sánchez, Félix;

An example regarding Kalton's paper ‘isomorphisms between spaces of vector-valued continuous functions’

Abstract

AbstractThe paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_{0}$ which is isomorphic to a closed subspace of a space with a basis and $C(I,\,X)$ is linearly homeomorphic to $C(\Delta ,\, X)$, then $X$ is locally convex, i.e., a Banach space. We will show that Kalton result is sharp by exhibiting non-locally convex quasi Banach spaces $X$ with a basis for which $C(I,\,X)$ and $C(\Delta ,\, X)$ are isomorphic. Our examples are rather specific and actually, in all cases, $X$ is isomorphic to $C(K,\,X)$ if $K$ is a metric compactum of finite covering dimension.

Related Organizations
Keywords

spaces of vector-valued continuous functions, Mathematics - Functional Analysis, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), 46A16, 46E10, General Topology (math.GN), FOS: Mathematics, Topological linear spaces of continuous, differentiable or analytic functions, quasi Banach spaces, Mathematics - General Topology, Functional Analysis (math.FA)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green