All automorphisms of the Calkin algebra are inner
Operator Algebras
2010-05-25 v9 Logic
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.
Keywords
Cite
@article{arxiv.0705.3085,
title = {All automorphisms of the Calkin algebra are inner},
author = {Ilijas Farah},
journal= {arXiv preprint arXiv:0705.3085},
year = {2010}
}
Comments
Only some minor changes