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.
@article{bwmeta1.element.bwnjournal-article-smv130i3p293bwm,
author = {W. \.Zelazko},
title = {A density theorem for algebra representations on the space (s)},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {293-296},
zbl = {0928.47012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p293bwm}
}
Żelazko, W. A density theorem for algebra representations on the space (s). Studia Mathematica, Tome 129 (1998) pp. 293-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p293bwm/
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