Singly generated operator algebras satisfying weakened versions of amenability

Abstract

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.

arXiv commentAMS-LaTeX. v1: 10 pages. v2: 12 pages; abstract revised, some typos corrected, some references added; Section 2 improved in response to referee's comments/corrections. v3: title on arXiv corrected to agree with title in the document. Final version, to appear in conference proceedings

References in corpus (2)

• Approximate and pseudo-amenability of various classes of Banach algebras
• On commutative, operator amenable subalgebras of finite von Neumann algebras