Marcoux, Laurent2024-01-312024-01-312022-11-03https://doi.org/10.1007/s11785-022-01296-7http://hdl.handle.net/10012/20324This is a post-peer-review, pre-copyedit version of an article published in Complex Analysis and Operator Theory. The final authenticated version is available online at: https://doi.org/10.1007/s11785-022-01296-7A number of questions which have been solved over the years in the theory of single operators acting on Hilbert space have interesting analogues when recast in the setting of elements of C*-algebras. We list five of these, as well as a number of "sub-problems" arising from them.ennilpotentsbiquasitriangularalgebraic elementscommutatorsSpecht's theoremsimilarity orbitsArticle