Let $E_n$ be a family of Banach spaces. Under which conditions imposed on $(E_n)$ can we represent the $\ell_\infty$-sum $(\bigoplus_{n\in \mathbb{N}} E_n)_{\ell_\infty}$ as a complemented subspace of some inductive limit of $(E_n)$? I do not require the inductive limits to be Banach spaces.
2026-04-02 18:35:31.1775154931
Inductive limits
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