A note on the Akemann-Doner and Farah-Wofsey constructions
Operator Algebras
2017-02-10 v1 Functional Analysis
Logic
Abstract
We remove the assumption of the continuum hypothesis from the Akemann-Doner construction of a non-separable -algebra with only separable commutative -subalgebras. We also extend a result of Farah and Wofsey's, constructing commuting projections in the Calkin algebra with no commutative lifting. This removes the assumption of the continuum hypothesis from a version of a result of Anderson. Both results are based on Luzin's almost disjoint family construction.
Keywords
Cite
@article{arxiv.1602.02429,
title = {A note on the Akemann-Doner and Farah-Wofsey constructions},
author = {Tristan Bice and Piotr Koszmider},
journal= {arXiv preprint arXiv:1602.02429},
year = {2017}
}