The paper “Characterization of dominated splittings for operator cocycles acting on Banach spaces” co-authored by Alex Blumenthal (Maryland) and Ian Morris has just been published in the Journal of Differential Equations. The paper gives a partial extension of a criterion of Bochi and Gourmelon for the existence of a dominated splitting of a finite-dimensional linear cocycle over a dynamical system to the case of infinite-dimensional cocycles acting on Banach spaces.  Alex Blumenthal was a PhD student of Lai-Sang Young (Courant Institute), is currently a postdoc at Maryland, and takes up an Assistant Professorship at Georgia Tech in the Autumn.  A link to the published paper is here.