Continuous Reinhardt domains from a Jordan viewpoint

L. L. Stachó. "Continuous Reinhardt domains from a Jordan viewpoint." Studia Mathematica 185.2 (2008): 177-199. <http://eudml.org/doc/284701>.

@article{L2008,
abstract = {As a natural extension of bounded complete Reinhardt domains in $ℂ^\{N\}$ 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.},
author = {L. L. Stachó},
journal = {Studia Mathematica},
keywords = {Jordan triple; holomorphic automorphism; commutative; -algebra; continuous Reinhardt domain; bidual; derivation},
language = {eng},
number = {2},
pages = {177-199},
title = {Continuous Reinhardt domains from a Jordan viewpoint},
url = {http://eudml.org/doc/284701},
volume = {185},
year = {2008},
}

TY - JOUR
AU - L. L. Stachó
TI - Continuous Reinhardt domains from a Jordan viewpoint
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 2
SP - 177
EP - 199
AB - As a natural extension of bounded complete Reinhardt domains in $ℂ^{N}$ 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.
LA - eng
KW - Jordan triple; holomorphic automorphism; commutative; -algebra; continuous Reinhardt domain; bidual; derivation
UR - http://eudml.org/doc/284701
ER -