Free and projective Banach lattices

Title

Free and projective Banach lattices

 Author

de Pagter, B. (TU Delft Analysis)
Wickstead, Anthony W. (Queen's University Belfast)

Date

2015

 Abstract

We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties. We give much more detailed results about their structure in the case when there are only a finite number of generators, and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice P to be projective if, whenever X is a Banach lattice, J is a closed ideal in X, Q : X → X/J is the quotient map, T : P → X/J is a linear lattice homomorphism and ε > 0, there exists a linear lattice homomorphism : P → X such that T = Q º and ∥∥ ≤ (1 + ε)∥T∥. We establish the connection between projective Banach lattices and free Banach lattices, describe several families of Banach lattices that are projective and prove that some are not.

 To reference this document use:

http://resolver.tudelft.nl/uuid:b6caf6f0-5327-4531-9836-d7846e98df30

 DOI

https://doi.org/10.1017/S0308210512001709

 Embargo date

2015-08-01

 ISSN

0308-2105

 Source

Royal Society of Edinburgh. Proceedings. Section A(Mathematics), 145 (1), 105-143

 Bibliographical note

Accepted author manuscript

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2015 B. de Pagter, Anthony W. Wickstead
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