On centralizers of an \(H^*\)-algebra. (English) Zbl 0860.46037
Summary: It is shown that the additive function \(T\) acting on a semisimple \(H^*\)-algebra \(\mathcal A\) with the property that \(T(x^3)= T(x)x^2\) \((x\in{\mathcal A})\) is a left centralizer.
MSC:
| 46K15 | Hilbert algebras |
| 47L10 | Algebras of operators on Banach spaces and other topological linear spaces |
| 39B42 | Matrix and operator functional equations |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 16N60 | Prime and semiprime associative rings |
