Injective Banach lattices: A survey

Abstract

The work is aimed to survey recent results on injective Banach lattices, outline the Boolean-valued approach, and pose some open problems. The central idea of the investigation is the Boolean-valued transfer principle from AL-spaces to injective Banach lattices: Every injective Banach lattice is embedded into an appropriate Boolean-valued model, becoming an AL-space. To illustrate the method, a concrete description of injective Banach lattices similar to that of AL-spaces is presented and the isometric classification of injective Banach lattices is accomplished.