Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774791 | Journal of Mathematical Analysis and Applications | 2017 | 17 Pages |
Abstract
Examples constructed by the first author and Charles Read make it clear that many of the hereditary properties of amenability no longer hold for approximate amenability. These and earlier results of the authors also show that the presence of a bounded approximate identity often entails positive results. Here we show that the tensor product of approximately amenable algebras need not be approximately amenable, and investigate conditions under which A and B being approximately amenable implies, or is implied by, AâËB or A#âËB# being approximately amenable. Once again, the rôle of having a bounded approximate identity comes to the fore. Our methods also enable us to prove that if AâËB is amenable, then so are A and B, a result proved by Barry Johnson in 1996 under an additional assumption.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
F. Ghahramani, R.J. Loy,