PreprintCC BY 4.0arXiv
Non-separable combinatorial Banach spaces
Abstract
We study combinatorial Banach spaces, i.e. Banach spaces induced by families of finite sets, of uncountable density. We prove some general theorems, for example we characterize when such spaces contain isomorphic copies of long c0 and long ℓ1. We discuss the existence of Banach spaces which are (complementedly) universal in the category of Banach spaces with unconditional basis of fixed cardinality. We present some examples, in particular we show that the Banach spaces generated by Suslin trees do not contain uncountable equilateral sets.
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BibTeX
@misc{borodulinnadzieja2026nonseparable,
title = {{Non-separable combinatorial Banach spaces}},
author = {Piotr Borodulin-Nadzieja and Mikołaj Marsy and Kamil Ryduchowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01919},
eprint = {2610.01919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01919},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-separable combinatorial Banach spaces
AU - Piotr Borodulin-Nadzieja
AU - Mikołaj Marsy
AU - Kamil Ryduchowski
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01919
UR - https://arxiv.org/abs/2610.01919
AB - We study combinatorial Banach spaces, i.e. Banach spaces induced by families of finite sets, of uncountable density. We prove some general theorems, for example we characterize when such spaces contain isomorphic copies of long c_0 and long ℓ_1. We discuss the existence of Banach spaces which are (complementedly) universal in the category of Banach spaces with unconditional basis of fixed cardinality. We present some examples, in particular we show that the Banach spaces generated by Suslin trees do not contain uncountable equilateral sets.
ER -