2021/03/15 by Avilés, Antonio, Martínez-Cervantes, Gonzalo, Abellán, José David Rodríguez +1
#06D05 #46B42 #54C55 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B20 #Secondary 06B25
paper · doi:10.48550/arxiv.2103.08170
In this article we deal with the free Banach lattice FBL⟨ \mathbbL ⟩ generated by a lattice \mathbbL. We prove that if FBL⟨ \mathbbL ⟩ is projective then \mathbbL has a maximum and a minimum. On the other hand, we show that if \mathbbL has maximum and minimum then FBL⟨ \mathbbL ⟩ is 2-lattice isomorphic to a C(K)-space. As a consequence, FBL⟨ \mathbbL ⟩ is projective if and only if it is lattice isomorphic to a C(K)-space with K being an absolute neighborhood retract. As an application, we characterize those linearly ordered sets and Boolean algebras for which the corresponding free Banach lattice is projective.