G. Cai

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math.FA2026

Hereditary Approximation under Hilbertian Extension

Gang Cai, Qingjin Cheng, Longfa Sun +1

In this paper, we prove that if a Banach space $X$ has the hereditary approximation property, then $X \oplus_{2} H$ has the hereditary approximation property for every Hilbert space $…

math.FA2026

Very tight embeddings of subspaces of $L_p$ for $0<p<1$

Gang Cai, Longfa Sun

For $0<p<1$ and $μ>1$, every $d$-dimensional subspace of $L_p$ embeds linearly into $\ell_p^{\lfloorμd\rfloor}$ with distortion at most $C(p,μ)(\log(d+2))^{1/p}$. If it…

Hereditary Approximation under Hilbertian Extension

Very tight embeddings of subspaces of \(L_p\) for \(0<p<1\)