Banach spaces & Banach lattices Seminar
Regular embeddings of AM-spaces
Speaker: Eugene Bilokopytov (ICMAT)Date: Friday, 23 October 2026 - 12:00Place: Aula Gris 3, ICMAT
Abstract:
Let \(E\) be an AM-space, let \(X_E\) be the set of all real-valued homomorphisms on \(E\) and let \(K_E:=X_E\cap B_{E^{}}\). We endow these sets with the bounded weak topology (on \(K_E\) it agrees with the weak* topology). Then \(E\) embeds into \(C(X_E)\) and \(C(K_E)\) in a natural way. Theorem. The embedding of \(E\) into \(C(X_E)\) is always order continuous (i.e. \(E\) is always a regular sublattice of \(C(X_E)\)). Also, \(E\) is a regular sublattice of \(C(K_E)\) iff \(E\) is order semicontinuous (a.k.a. Fatou).
