A density theorem for algebra representations on the space (s)
Volume 130 / 1998
Studia Mathematica 130 (1998), 293-296 DOI: 10.4064/sm-130-3-293-296
We show that an arbitrary irreducible representation T of a real or complex algebra on the F-space (s), or, more generally, on an arbitrary infinite (topological) product of the field of scalars, is totally irreducible, provided its commutant is trivial. This provides an affirmative solution to a problem of Fell and Doran for representations on these spaces.