This is an announcement for the paper "Free and projective Banach lattices" by B. de Pagter and A.W. Wickstead.

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 that 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, $J$ a closed ideal in $X$, $Q:X\to X/J$ the quotient map, $T:P\to X/J$ a linear lattice homomorphism and $\epsilon>0$ there is a linear lattice homomorphism $\hat{T}:P\to X$ such that (i) $T=Q\circ \hat{T}$ and (ii) $|\hat{T}|\le (1+\epsilon)|T|$. We establish the connection between projective Banach lattices and free Banach lattices and describe several families of Banach lattices that are projective as well as proving that some are not.

Archive classification: math.FA

Submitted from: A.Wickstead@qub.ac.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1204.4282

or

http://arXiv.org/abs/1204.4282