All automorphisms of all Calkin algebras

Abstract

The Proper Forcing Axiom implies all automorphisms of every Calkin algebra associated with an infinite-dimensional complex Hilbert space and the ideal of compact operators are inner. As a means of the proof we introduce the notion of Polish ${\omega }_1$-trees and cohrerent families of Polish spaces and prove some uniformization results.

arXiv commentTo appear in Math. Res. Letters