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A small Banach space C(K) without nice renormings
Abstract
We prove that consistently ω1<c and there exists a compact space K whose Banach space C(K) of continuous real-valued functions is Grothendieck, has density ω1, and admits no renorming which is strictly convex or sequentially Kadets--Klee.
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BibTeX
@misc{manev2026small,
title = {{A small Banach space $C(K)$ without nice renormings}},
author = {Todor Manev and Damian Sobota and Lyubomyr Zdomskyy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.13294},
eprint = {2606.13294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13294},
}
RIS
TY - UNPB
TI - A small Banach space C(K) without nice renormings
AU - Todor Manev
AU - Damian Sobota
AU - Lyubomyr Zdomskyy
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2606.13294
UR - https://arxiv.org/abs/2606.13294
AB - We prove that consistently ω_1<c and there exists a compact space K whose Banach space C(K) of continuous real-valued functions is Grothendieck, has density ω_1, and admits no renorming which is strictly convex or sequentially Kadets--Klee.
ER -