Symmetric continuous Reinhardt domains

Abstract

We extend the concept of Reinhardt domains to complex function spaces and we give a complete parametric description of all bounded symmetric Reinhardt domains in a C 0 -space.

Continuous Reinhardt domains from a Jordan viewpoint

“…In [17] we have shown that a symmetric CRD is a continuous mixture of finite-dimensional Euclidean balls, essentially more involved than direct sums of topological products of balls. In [7] we found matrix representations for linear isomorphisms between two symmetric CRDs.…”

“…Later on several authors investigated holomorphic equivalence of generalized Reinhardt domains in atomic Banach lattices [1,2,12]. Motivated by an interesting work of Vigué [19] on the possible lack of symmetry of continuous products of discs with different radii, in [17] we introduced the concept of continuous Reinhardt domains (CRD for short).…”

Bicircular projections and characterization of Hilbert spaces

“…These are open subsets of C 0 (Ω), satisfying some additional properties (cf. [18]). In [18] we were led, at some technical point, to study projections with one-dimensional range and additional norm property, which is called bicircularity.…”

“…[18]). In [18] we were led, at some technical point, to study projections with one-dimensional range and additional norm property, which is called bicircularity. What we needed to show was that their kernels are Hilbert spaces.…”

“…We thus expand, what was a technical point in [18], into an independent study in its proper algebraic setting, which is that of JB* triples. Our main result and its corollary can be interpreted as a characterization of Hilbert spaces among JB* triples.…”