Banach lattices of positively homogeneous functions induced by a Banach space

Laustsen, Niels and Tradacete, Pedro (2025) Banach lattices of positively homogeneous functions induced by a Banach space. Proceedings of the Edinburgh Mathematical Society. ISSN 0013-0915 (In Press)

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Abstract

Motivated by the construction of the free Banach lattice generated by a Banach space, we introduce and study several vector and Banach lattices of positively homogeneous functions defined on the dual of a Banach space E. The relations between these lattices allow us to give multiple characterizations of when the underlying Banach space E is finite-dimensional and when it is reflexive. Furthermore, we show that lattice homomorphisms between free Banach lattices are always composition operators, and study how these operators behave on the scale of lattices of positively homogeneous functions.

Item Type:

Journal Article

Journal or Publication Title:

Proceedings of the Edinburgh Mathematical Society

Uncontrolled Keywords:

Research Output Funding/yes_externally_funded

Subjects:

?? banach latticebanach spacefree banach latticelattice homomorphismyes - externally fundednomathematics(all) ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

232960

Deposited By:

ep_importer_pure

Deposited On:

10 Oct 2025 15:35

Refereed?:

Yes

Published?:

In Press

Last Modified:

05 Dec 2025 00:53

URI:

https://eprints.lancs.ac.uk/id/eprint/232960