## Singly generated operator algebras satisfying weakened versions of amenability

#### Authors

Yemon Choi

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

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

#### Status

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

#### Reviews

[ 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.