A negative solution to the complemented subspace problem in Banach lattices

2023/10/03 by de Hevia, D., Martínez-Cervantes, G., Salguero-Alarcón, A. +1 · 2 citations
#46B03 #46B42 #46E15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2310.02196

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.

Cited by

• C(K)-spaces with few operators relative to posets
• The class of Banach lattices is not primary

Related

• Complemented subspaces of Banach lattices
• The class of Banach lattices is not primary
• The Banach space S is complementably minimal and subsequentially prime
• The complemented subspace problem for C(K)-spaces: A counterexample
• K(X,Y) as subspace complemented of L(X,Y)