One-sided division absolute valued algebras
ISSN: 0214-1493
Año de publicación: 1992
Título del ejemplar: la memória de Pere Menal i Brufal
Volumen: 36
Número: 2
Páginas: 925-954
Tipo: Artículo
Otras publicaciones en: Publicacions matematiques
Resumen
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.