PreprintCC BY 4.0arXiv
Order continuity of induced homomorphisms between free Banach lattices
Abstract
Let T: F→ E be a bounded operator between Banach spaces and let T̅: FBL(p)[F]→ FBL(p)[E] be the lattice homomorphism induced by T between the corresponding free p-convex Banach lattices generated by F and E. We show that T̅ is order continuous if and only if it is either zero or a lattice isomorphic embedding. For p=∞, this holds precisely when T is zero or an isomorphic embedding, while for 1≤ p<∞, apart from the zero operator, T must be an embedding and the pair (T(F),E) must have the operator-extension property POE-p. In addition, we study when FBL(p)[E] is order dense or majorizing in FBL(q)[E] for p<q.
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BibTeX
@misc{parientemartin2026order,
title = {{Order continuity of induced homomorphisms between free Banach lattices}},
author = {Raúl E. Pariente-Martín and Pedro Tradacete},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00451},
eprint = {2611.00451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00451},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Order continuity of induced homomorphisms between free Banach lattices
AU - Raúl E. Pariente-Martín
AU - Pedro Tradacete
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00451
UR - https://arxiv.org/abs/2611.00451
AB - Let T: F→ E be a bounded operator between Banach spaces and let T̅: FBL^(p)[F]→ FBL^(p)[E] be the lattice homomorphism induced by T between the corresponding free p-convex Banach lattices generated by F and E. We show that T̅ is order continuous if and only if it is either zero or a lattice isomorphic embedding. For p=∞, this holds precisely when T is zero or an isomorphic embedding, while for 1≤ p<∞, apart from the zero operator, T must be an embedding and the pair (T(F),E) must have the operator-extension property POE-p. In addition, we study when FBL^(p)[E] is order dense or majorizing in FBL^(q)[E] for p<q.
ER -