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arXiv · 2310.02196

A negative solution to the complemented subspace problem in Banach lattices

D. de Hevia·G. Martínez-Cervantes·A. Salguero-Alarcón·P. Tradacete
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Abstract

Building on a recent construction of G. Plebanek and the third named author, it is shown that a complemented subspace of a Banach lattice need not be linearly isomorphic to a Banach lattice. This solves a long-standing open question in Banach lattice theory.

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D. de Hevia, G. Martínez-Cervantes, A. Salguero-Alarcón, P. Tradacete. 2023-10-03. A negative solution to the complemented subspace problem in Banach lattices. https://arxiv.org/abs/2310.02196

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