×

zbMATH — the first resource for mathematics

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].
MSC:
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
PDF BibTeX Cite
Full Text: DOI arXiv