The free p-convex Banach lattice FBL^(p)[E] over a Banach space E is the p-convex Banach lattice generated by an isometric copy of E in which every norm-one operator from E into a p-convex Banach lattice extends uniquely to a lattice homomorphism of the same norm. Students learn its functional representation as positively homogeneous weak-star continuous functions on the dual of E, how properties of an operator between Banach spaces transfer to the induced lattice homomorphism, and the dictionary translating Banach space properties of E into lattice properties of FBL^(p)[E] - strong units and finite dimensionality, quasi-interior points and separability, lattice copies of l_1 and complemented copies of l_1, and upper p-estimates and (q,1)-summing identities.
The free p-convex Banach lattice FBL^(p)[E] over a Banach space E is the p-convex Banach lattice that contains an isometric copy of E, is generated by that copy as a lattice, and satisfies a universa…