This is an announcement for the paper “Valuations on Banach lattices” by Pedro Tradacetehttps://arxiv.org/find/math/1/au:+Tradacete_P/0/1/0/all/0/1, Ignacio Villanuevahttps://arxiv.org/find/math/1/au:+Villanueva_I/0/1/0/all/0/1.

Abstract: We provide a general framework for the study of valuations on Banach lattices. This complements and expands several recent works about valuations on function spaces, including $L_p(\mu)$, Orlicz spaces and spaces $C(K)$ of continuous functions on a compact Hausdorff space. In particular, we study decomposition properties, boundedness and integral representation of continuous valuations.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1711.11558