analysis / Banach Space Decomposition Theory

Primariness of the Mixed-Norm Space $L_p(L_1)$

A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of $L_p(L_1)$ as a prominent remaining open case; the paper proves it is primary for $1<p<\infty$.

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analysisJul 19, 2026Significance 20/100Registry: unreviewed

Primariness of the Mixed-Norm Space $L_p(L_1)$

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A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of $L_p(L_1)$ as a prominent remaining open case; the paper proves it is primary for $1<p<\infty$.

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A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of $L_p(L_1)$ as a prominent remaining open case; the paper proves it is primary for $1<p<\infty$.

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