To answer your questions:

1) I consider two *concrete* operator algebras and (maybe different and ), and then similarity means the usual thing (see definition above the Clouatre-Ramsey trick that I added now).

2) Surely that’s not exactly what you meant to ask (because it is plainly false, even for C*-algebras). If you wanted to ask whether a completely contractive homomorphism that has a completely bounded inverse must completely contractive then the answer is no (the inverse of , where is an appropriately chosen completely bounded map but not contractive map can serve as an example).

]]>I have mixed feelings about mixed conferences. But since I haven’t really decided what I myself want to be working on when I grow up, I think they work for me.

since I feel similarly…

]]>Something about the way you state this made me laugh (not that I am disagreeing). It’s certainly got more going on than, say, Waterloo 🙂

The conference sounds interesting – unfortunately the timing of both CAHAS and COSY doesn’t really work well for me now that I am working in the UK. I would have liked to talk similarity problems with Chris and Raphael.

Small note/queries:

1) I guess that by similarity you mean “similarity inside B(H) for a suitable choice of embeddings into B(H)”?

2) I may be missing something, but is it clear that a completely contractive surjection has completely contractive inverse? Is this even true?

]]>I taught once a course in Fourier analysis for engineers which (clearly) had not functional analysis or measure theory prerequisite, though some of the methods or modes of thinking of functional analysis were introduced along the way.

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