Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
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TY - CHAP
T1 - Singly generated operator algebras satisfying weakened versions of amenability
AU - Choi, Yemon
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Approximate amenability
KW - biflatness
KW - compact operators
KW - finite von Neumann algebra
KW - monogenic Banach algebra
KW - Type I von Neumann algebra
U2 - 10.1007/978-3-0348-0502-5_3
DO - 10.1007/978-3-0348-0502-5_3
M3 - Chapter
SN - 9783034805018
T3 - Operator Theory: Advances and Applications
SP - 33
EP - 44
BT - Algebraic methods in functional analysis
A2 - Todorov, Ivan G.
A2 - Turowska, Lyudmila
PB - Springer Verlag
CY - Basel
ER -