A negative solution to the complemented subspace problem in Banach lattices
Functional Analysis
2025-04-07 v2
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.
Keywords
Cite
@article{arxiv.2310.02196,
title = {A negative solution to the complemented subspace problem in Banach lattices},
author = {D. de Hevia and G. Martínez-Cervantes and A. Salguero-Alarcón and P. Tradacete},
journal= {arXiv preprint arXiv:2310.02196},
year = {2025}
}