Isomorphisms from Extremely Regular Subspaces of into Spaces

Manuel Felipe Cerpa-Torres and Michael A. Rincón-Villamizar

International Journal of Mathematics and Mathematical Sciences, 2019, vol. 2019, 1-7

Abstract:

For a locally compact Hausdorff space K and a Banach space X , let be the Banach space of all X -valued continuous functions defined on K , which vanish at infinite provided with the sup norm. If X is , we denote as . If be an extremely regular subspace of and is an into isomorphism, what can be said about the set-theoretical or topological properties of K and S ? Answering the question, we will prove that if X contains no copy of , then the cardinality of K is less than that of S . Moreover, if and is also a subalgebra of , the cardinality of the α th derivative of K is less than that of the α th derivative of S , for each ordinal Finally, if and , then K is a continuous image of a subspace of S . Here, is the geometrical parameter introduced by Jarosz in 1989: As a consequence, we improve classical results about into isomorphisms from extremely regular subspaces already obtained by Cengiz.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7146073

DOI: 10.1155/2019/7146073

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