Sometimes the real world and the blogosphere intersect, as they did yesteray.

Yemon Choi, from Saskatchewan, whose blog Since it is not … has been on my sidebar for quite some time and has survived my occasional culls, gave a talk at Queen Mary entitled “Commutative amenable operator algebras”. The talk had been advertised as “out-of-exam entertainment”: how could I resist?

Banach algebras are not my field, but I suspected that bloggers on average give better talks than non-bloggers. This one certainly confirmed the theory.

It was subtitled “A partial survey”, and Yemon explained that this had two meanings: he was not covering everything, and he is not impartial about the topic.

I thought it was brave to go from 2×2 matrices on the second slide to amenable groups on the third; but it was all slowly and clearly explained on the board, and I was able to get a feel for what is going on. There is a notion of amenable Banach algebra, one whose representations have a kind of Maschke property, closed invariant subspaces have invariant complements. (That isn’t the definition!)

I must apologise publicly to Yemon that I couldn’t stay after the talk; I had to dash off to the next thing. (So much for leisurely retirement!)

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## About Peter Cameron

I count all the things that need to be counted.

Thanks for the mention, Peter. No need to apologize! It was a pleasant surprise to see you there and I’m glad you were able to get something from the talk. One is never quite sure what kind of audience to expect.

“Amenability as some kind of Maschke” is a point of view that I have unofficially held, albeit in a timid way, for some time now. (I don’t claim any originality, this is really the “vanishing Ext” definition of Helemskii et al. in a special case.)