PreprintarXiv licencearXiv
A Vector-Valued Extension of a Theorem of Marciszewski
Abstract
We establish a vector-valued extension of a theorem of Marciszewski. Let K be a compact Hausdorff space, let Γ be a set, and let X be a nonzero Banach space containing no isomorphic copy of c0. We prove that if C(K) embeds isomorphically into c0(Γ,X), then C(K) is isomorphic to c0(Λ) for some set Λ. Moreover, when Γ is infinite, the optimal distortion of embeddings of C(K) into c0(Γ,X) equals that of embeddings into c0(Γ). The classification result answers a question posed in an earlier paper.
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BibTeX
@misc{candido2026vectorvalued,
title = {{A Vector-Valued Extension of a Theorem of Marciszewski}},
author = {Leandro Candido},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13414},
eprint = {2610.13414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13414},
}
RIS
TY - UNPB
TI - A Vector-Valued Extension of a Theorem of Marciszewski
AU - Leandro Candido
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13414
UR - https://arxiv.org/abs/2610.13414
AB - We establish a vector-valued extension of a theorem of Marciszewski. Let K be a compact Hausdorff space, let Γ be a set, and let X be a nonzero Banach space containing no isomorphic copy of c_0. We prove that if C(K) embeds isomorphically into c_0(Γ,X), then C(K) is isomorphic to c_0(Λ) for some set Λ. Moreover, when Γ is infinite, the optimal distortion of embeddings of C(K) into c_0(Γ,X) equals that of embeddings into c_0(Γ). The classification result answers a question posed in an earlier paper.
ER -