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.
Mathematics Subject Classification (2010). 47L75 (primary); 46J40 (secondary).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to V.S. Shulman on the occasion of his 65th birthday
Rights and permissions
Copyright information
© 2014 Springer Basel
About this paper
Cite this paper
Choi, Y. (2014). Singly Generated Operator Algebras Satisfying Weakened Versions of Amenability. In: Todorov, I., Turowska, L. (eds) Algebraic Methods in Functional Analysis. Operator Theory: Advances and Applications, vol 233. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0502-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0502-5_3
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0501-8
Online ISBN: 978-3-0348-0502-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)