Coarse embeddings into $c_0(Γ)$
Year: 2017
Type: preprint
Abstract: Let $λ$ be a large enough cardinal number (assuming GCH it suffices to let $λ=\aleph_ω$). If $X$ is a Banach space with $\text{dens}(X)\geλ$, which admits a coarse (or uniform) embedding into any $c_0(Γ)$, then $X$ fails to have nontrivial cotype, i.e. $X$ contains $\ell_\infty^n$ $C$-uniformly for every $C>1$. In the special case when $X$ has a symmetric basis, we may even conclude that it is linearly isomorphic with $c_0(\text{dens}X)$.
Source: arXiv (Cornell University)
Authors: Hajek, Petr, Schlumprecht, Thomas
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394651111