We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution τ such that A = {b ∈ B : τ(b) = b*}. Using this, we obtain our main result, namely: (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically isomorphic.
@article{urn:eudml:doc:41059,
title = {Nonassociative real H*-algebras.},
journal = {Publicacions Matem\`atiques},
volume = {32},
year = {1988},
pages = {267-274},
mrnumber = {MR0975901},
zbl = {0673.46035},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41059}
}
Cabrera, Miguel; Martínez Aroza, José; Rodríguez Palacios, Angel. Nonassociative real H*-algebras.. Publicacions Matemàtiques, Tome 32 (1988) pp. 267-274. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41059/