On embeddings of C₀(K) spaces into C₀(L,X) spaces

• Autorzy: Leandro Candido
• Języki publikacji: EN

Abstrakty

EN

For a locally compact Hausdorff space K and a Banach space X let C₀(K, X) denote the space of all continuous functions f:K → X which vanish at infinity, equipped with the supremum norm. If X is the scalar field, we denote C₀(K, X) simply by C₀(K). We prove that for locally compact Hausdorff spaces K and L and for a Banach space X containing no copy of c₀, if there is an isomorphic embedding of C₀(K) into C₀(L,X), then either K is finite or |K| ≤ |L|. As a consequence, if there is an isomorphic embedding of C₀(K) into C₀(L,X) where X contains no copy of c₀ and L is scattered, then K must be scattered.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 1-6

Daty

wydano

2016

Twórcy

autor

Leandro Candido

• Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo, Campus São José dos Campos - Parque Tecnológico, Avenida Cesare Monsueto Giulio Lattes, 1211, 12231-280 São José dos Campos - SP, Brazil

Identyfikatory

DOI

10.4064/sm7857-3-2016