This project is mathematical research on a class of objects, known as Banach Jordan triple systems or JB*-triples, that are Banach spaces equipped with a compatible ternary product satisfying certain algebraic conditions. Their study thus incorporates geometry in infinitely many dimensions, and a species of nonassociative algebra. As the use of Jordan's name suggests, these structures have applications in mathematical physics and the foundations of quantum mechanics. Strictly within mathematics, many useful consequences can be extracted once one knows that a given convex set is in fact the unit ball of a JB*-triple. One specific objective of the research is to characterize geometrically the Banach spaces that are duals of JB*-triples. Derivations, bounded and unbounded, of JB*-triples will also be studied. Finally, the manifold consequences of changing the underlying field of scalars from the complex numbers to the real numbers will be explored.
