Continuous Reinhardt domains from a Jordan viewpoint

L. L. Stachó¹

¹ Bolyai Institute Aradi Vértanúk tere 1 H-6725 Szeged, Hungary

Studia Mathematica, Tome 185 (2008) no. 2, pp. 177-199

Résumé

As a natural extension of bounded complete Reinhardt domains in ${{\mathbb C}}^N$ to spaces of continuous functions, continuous Reinhardt domains (CRD) are bounded open connected solid sets in commutative $C^*\! $-algebras with respect to the natural ordering. We give a complete parametric description for the structure of holomorphic isomorphisms between CRDs and characterize the partial Jordan triple structures which can be associated with some CRDs. On the basis of these results, we test two conjectures concerning the Jordan structure of bounded circular domains. It turns out that both the problems of bidualization and unique extension of inner derivations have positive solution in the setting of CRDs.

Détail

DOI : 10.4064/sm185-2-6

Keywords: natural extension bounded complete reinhardt domains mathbb spaces continuous functions continuous reinhardt domains crd bounded connected solid sets commutative * algebras respect natural ordering complete parametric description structure holomorphic isomorphisms between crds characterize partial jordan triple structures which associated crds basis these results test conjectures concerning jordan structure bounded circular domains turns out problems bidualization unique extension inner derivations have positive solution setting crds