We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation Relations" in Quantum Mechanics. We also show that homomorphisms from complete normed algebras into arbitrary absolute valued algebras are contractive, hence automatically continuous.
@article{urn:eudml:doc:41761,
title = {One-sided division absolute valued algebras.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {925-954},
mrnumber = {MR1210027},
zbl = {0797.46040},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41761}
}
Rodríguez Palacios, Ana. One-sided division absolute valued algebras.. Publicacions Matemàtiques, Tome 36 (1992) pp. 925-954. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41761/