Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701A Kakutani-Mackey-like theorem5075215602910.15352/aot.1712-1270ENMarina HaralampidouDepartment of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, GreeceKonstantinos TzironisDepartment of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, GreeceJournal Article20171205We give a partial extension of a Kakutani-Mackey theorem for quasi-complemented vector spaces. This can be applied in the representation theory of certain complemented (non-normed) topological algebras. The existence of continuous linear maps, in the context of quasi-complemented vector spaces, is a very important issue in their study. Relative to this, we prove that every Hausdorff quasi-complemented locally convex space has continuous linear maps, under which a certain quasi-complemented locally convex space, turns to be pre-Hilbert.<br /><br />http://www.aot-math.org/article_56029_e54f74797c92d1f650c19dab2b77f90e.pdf