Poisson structure on predual of Banach Lie algebroid

Abstract

We construct the linear Poisson bracket on the predual bundle of a Banach Lie algebroid. It is an alternative approach to the already known results on the linear sub-Poisson structure on the dual bundle. We also discuss the existence of queer Banach Lie algebroids. The example on a trivial bundle is presented and the situation on precotangent bundles is discussed.

24 pages