Homomorphisms and Higher Derivations on Banach-Jordan Systems

Jordan Pairs and Jordan triple systems are an extension of Jordan algebras and ternary rings. They are principal algebraic structures in Jordan Theory and nonassociative algebra. Jordan pairs arise in a natural way in the geometry of bounded symmetric domains. O. Loos proved a strong dependence between homogeneous circled domains, in finite-dimensional complex vector spaces, and Jordan pairs. Operators defined on Jordan pairs play prominent role in their study specially in the case of normed or Banach-Jordan Pairs. In this situation, the automatic continuity of these operators together with their structures in some classes of Jordan Pairs arise as an interesting problem in a branch of functional analysis.