Free and projective Banach lattices

Anthony Wickstead, Ben de Pagter

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

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 thatT = 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.
Original languageEnglish
Pages (from-to)105-143
Number of pages39
JournalProceedings of the Royal Society of Edinburgh. Section A. Mathematics
Volume145
Issue number1
Early online date30 Jan 2015
Publication statusPublished - Feb 2015

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