Nonassociative real $H^*$-algebras

M. Cabrera, J. Martínez, A. Rodríguez
1988 Publicacions matemàtiques  
NONASSOCIATIVE REAL H*-ALGEBRAS M . CABRERA, J . MARTÍNEZ, A . RODRÍGUEZ 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 r such that A = {b E B : r(b) = b*} . Using this, we obtain our main result, namely : (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically
more » ... lly *-isometrically isomorphic .
doi:10.5565/publmat_32288_10 fatcat:lilcnf5qxjabnjfyeszmrwo6zy