Lin solved a longstanding problem as follows. For each , there is such that, if and are self-adjoint contractive matrices and , then there are commuting self-adjoint matrices and such that , . Here depends only on and not on . Friis and Rørdam greatly simplified Lin’s proof by using a property they called . They also generalized Lin’s result by showing that the matrix algebras can be replaced by any -algebras satisfying . The purpose of this paper is to study the property . One of our results shows how behaves for -algebra extensions. Other results concern nonstable -theory. One shows that (at least the stable version) implies a cancellation property for projections which is intermediate between the strong cancellation satisfied by -algebras of stable rank and the weak cancellation defined in a 2014 paper by Pedersen and the author.
"On the property of Friis and Rørdam." Banach J. Math. Anal. 13 (3) 599 - 611, July 2019. https://doi.org/10.1215/17358787-2019-0004