All automorphisms of the Calkin algebra are inner

Abstract

We prove that it is relatively consistent with the usual axioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips--Weaver construction of an outer automorphism using the Continuum Hypothesis, this gives a complete solution to a 1977 problem of Brown-Douglas-Fillmore. We also give a simpler and self-contained proof of the Phillips--Weaver result.

Only some minor changes

References in corpus (1)

• A five element basis for the uncountable linear orders

Cited by in corpus (3)

• On low rank perturbation of matrices
• Almost solutions of equations in permutations
• On the pointwise implementation of near-actions