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Apr 26, 2016 at 10:18 comment added Simon Henry Maybe you can do the same construction with $\alpha_p$ an endomorphism of $M_p(\mathbb{C})$ for each prime $p$ ? But you need to be more carefull on how you identify $M_n \otimes M_m$ with $M_{nm}$ to see if this works... I'm not convinced.
Apr 26, 2016 at 9:02 comment added Ali Taghavi Thanks for your very interesting answer. what about if a trivial sequence would be meant as "a sequence of scalar operator"? is there a non trivial example?
Apr 26, 2016 at 8:54 history answered Simon Henry CC BY-SA 3.0