Singly generated operator algebras satisfying weakened versions of amenability

Choi, Yemon (2014) Singly generated operator algebras satisfying weakened versions of amenability. In: Algebraic methods in functional analysis. Operator Theory: Advances and Applications . Springer Verlag, Basel, pp. 33-44. ISBN 9783034805018

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Abstract

We construct a singly generated subalgebra of K(H) which is nonamenable, 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 [3] to follow from amenability, does not necessarily imply amenability.

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Contribution in Book/Report/Proceedings
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ID Code:
68387
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Deposited On:
24 Jan 2014 06:09
Refereed?:
No
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Published
Last Modified:
01 Jan 2020 05:45