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Singly generated operator algebras satisfying weakened versions of amenability. (English) Zbl 1329.46045
Todorov, Ivan G. (ed.) et al., Algebraic methods in functional analysis. The Victor Shulman anniversary volume. Basel: Birkhäuser (ISBN 978-3-0348-0501-8/hbk; 978-3-0348-0502-5/ebook). Operator Theory: Advances and Applications 233, 33-44 (2014).
This paper is a continuation of the author’s previous work [J. Reine Angew. Math. 678, 201–222 (2013; Zbl 1282.46054)] and is motivated by the still open problem of characterizing operator algebras which are amenable as Banach algebras. The first example constructed by the author is a singly generated subalgebra of the set of all compact operators on Hilbert space which is non-amenable, yet is boundedly approximately contractible. It is also remarked that there are singly generated, biflat subalgebras of finite type I von Neumann algebras which are not amenable.
For the entire collection see [Zbl 1276.47002].
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46L10 General theory of von Neumann algebras
47L75 Other nonselfadjoint operator algebras
47L45 Dual algebras; weakly closed singly generated operator algebras
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