What question did this study set out to answer?

The research aims to assess the conjecture regarding the separably injective nature of ℓ∞/C[0,1].

March 31, 2026Open Access

All L_ -spaces are separably injective, kind of

Puntos clave

The research aims to assess the conjecture regarding the separably injective nature of ℓ∞/C[0,1].
Investigated the conjecture using homological terms and Ext groups.
Examined the relationship between Ext^2(S, C[0,1]) and separability.
Explored connections with classical Banach space theorems.
Found new links between Ext^2 results and established Banach space theorems.
Confirmed the conjecture under certain conditions for separable spaces.

Resumen

Abstract How reasonable is the conjecture that _ /C0, 1 ℓ ∞ / C 0, 1 separably injective? Formulated in homological terms this amounts to asking whether Ext² (S, C0, 1) =0 Ext 2 (S, C 0, 1) = 0 for every separable space. We wheel around this question and obtain new connections between Ext² Ext 2 -results and classical Banach space theorems of Johnson–Zippin, Kalton and Lindenstrauss–Pełczyński.

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