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

Leandro Candido. "On embeddings of C₀(K) spaces into C₀(L,X) spaces." Studia Mathematica 232.1 (2016): 1-6. <http://eudml.org/doc/285855>.

@article{LeandroCandido2016,
abstract = {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.},
author = {Leandro Candido},
journal = {Studia Mathematica},
keywords = {isomorphisms; linear embeddings; C0(K) spaces; C0(K; X) spaces},
language = {eng},
number = {1},
pages = {1-6},
title = {On embeddings of C₀(K) spaces into C₀(L,X) spaces},
url = {http://eudml.org/doc/285855},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Leandro Candido
TI - On embeddings of C₀(K) spaces into C₀(L,X) spaces
JO - Studia Mathematica
PY - 2016
VL - 232
IS - 1
SP - 1
EP - 6
AB - 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.
LA - eng
KW - isomorphisms; linear embeddings; C0(K) spaces; C0(K; X) spaces
UR - http://eudml.org/doc/285855
ER -