All $\mathcal L_\infty $-spaces are separably injective, kind of

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2026年3月29日

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Jesús M. F. Castillo,
Yolanda Moreno

摘要

How reasonable is the conjecture that $\ell _\infty /C[0,1]$ $ℓ_{\infty} / C [0, 1]$ separably injective? Formulated in homological terms this amounts to asking whether $\operatorname {Ext}^2(S, C[0,1])=0$ ${Ext}^{2} (S, C [0, 1]) = 0$ for every separable space. We wheel around this question and obtain new connections between $\operatorname {Ext}^2$ ${Ext}^{2}$ -results and classical Banach space theorems of Johnson–Zippin, Kalton and Lindenstrauss–Pełczyński.

All \(\mathcal L_\infty \)-spaces are separably injective, kind of

摘要