Real normed Jordan Banach algebras with an involution
The subject of the paper are the Jordan analogues of real \(C^*\)- algebras. A \(J^*B\)-algebra is a real Jordan algebra with unit and an involution * with a complete algebra norm such that \(\| U_ xx^*\| =\| x\|^ 3\) and \(\| x^*x\| \leq \| x^*x+y^*y\|.\) In the first part of the paper the complexification theorem is proved: the complexification of a \(J^*B\)-algebra is a \(JB^*\)-algebra. The second part treats the classification of the finite dimensional \(J^*B\)-algebras.
Jordan analogues of real \(C^*\)-algebras
classification of the finite dimensional \(J^*B\)-algebras
scientific article; zbMATH DE number 3929735