Octahedrality and G\^ateaux smoothness

Ch. Cobollo; P. Hájek

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arXiv · 2408.03737

Octahedrality and G\^ateaux smoothness

Ch. Cobollo·P. Hájek

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Abstract

We prove that every Banach space admitting a Gateaux smooth norm and containing a complemented copy of $\ell_1$ has an equivalent renorming which is simultaneously G\^ateaux smooth and octahedral. This is a partial solution to a problem from the early nineties.

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Ch. Cobollo, P. Hájek. 2024-08-07. Octahedrality and G\^ateaux smoothness. https://arxiv.org/abs/2408.03737

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