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Singly generated operator algebras satisfying weakened versions of amenability


Yemon Choi


MSC 2010: 47L75 (Primary), 46J40 (Secondary)

DOI: 10.1007/978-3-0348-0502-5_3


Appeared in the book Algebraic Methods in Functional Analysis
(proceedings of the Conference on Operator Theory and its Applications, Gothenburg, 26-29 April 2011, in honour of V. S. Shulman.).
Article details: Operator Theory: Advances and Applications, vol. 233 (2014), 33--44.

Preprint version available at arXiv 1204.6343


[ Math Review (summary) | Zentralblatt ]

Abstract (arXiv version)

We construct a singly generated subalgebra of ${\mathcal K}({\mathcal H})$ which is non-amenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, biflat subalgebras of finite Type I von Neumann algebras, which are not amenable (and hence are not isomorphic to C*-algebras). Such an example can be used to show that a certain extension property for commutative operator algebras, which is shown in arXiv:1012.4259 to follow from amenability, does not necessarily imply amenability.


The main construction in the first half of the paper arose while trying to find embeddings of certain weighted semilattice algebras as closed subalgebras of B(H). Trying to do this with the Feinstein algebras failed, but then I realised that suitable homomorphic images would still have closures that were approximately amenable without being amenable.

Yemon Choi