Carlo, It brought both tears and laughter! Still, I would like to see similar information for schools in the US.

Carlo, that's a start. I would like to see information about average rates. For example, is it more common for a graph theorist than an analyst to publish more than ten or more papers in 5 years? what about 15 or more papers?

I guess the answer to my question is: It's not known. It's an open problem.

$l^{\infty}(\mathbb{Z})$. The automorphisms have to preserve the $W^{*}$-algebra structure.

It doesn't sound like you are familiar with the $C^{*}$ envelope of an operator algebra. In the case of a dual operator algebra ,we have to consider the $W^{*}$ algebras generated by ALL weak$^{*}$ continuous completely isometric homomorphisms $j:A\to B$ such that $B$ is generated as a $W^{*}$-algebra by $j(A)$. From all these $W^{*}$-algebras, is there a minimal one?

I'm talking about an abstract dual operator algebra $A$ (that is, there is a Hilbert space H and a w$^{*}$-continuous completely isometric isomorphism $\pi:A\to B(H)$ ). I want to know if anybody has proven that there is a minimal $W^{*}$-algebra generated by $A$ (yes, considering all representations, just like in the case of the $C^{*}$-envelope of an operator algebra).

Thank you for the reply Rasmus. So if I understand correctly, a correspondence over $A$ generalizes a $C^{*}$-endomorphism $\varphi:A \to A$ because now the range of $\varphi$ does not have to be $A$ but it can be a $C^{*}$-algebra containing $A$ (the multiplier algebra of $A$). Does this make sense?

@RasmusBentmann: Can you please explain how morphisms induce correspondences and how composition extends to correspondences, or point me to a book/paper discussing this ? Thank you