Trace-order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional JB -triple

https://doi.org/10.1016/j.jmaa.2012.07.027Get rights and content
Under an Elsevier user license
open archive

Abstract

We give a distortion theorem for linearly invariant families on the unit ball B of a finite dimensional JB-triple X by using the trace-order. The exponents in the distortion bounds depend on the Bergman metric at 0. Further, we introduce a new definition for the trace-order of a linearly invariant family on B, based on a Jacobian argument. We also construct an example of a linearly invariant family on B which has minimum trace-order and is not a subset of the normalized convex mappings of B for dimX2. Finally, we prove a regularity theorem for linearly invariant families on B. All four types of classical Cartan domains are the open unit balls of JB-triples, and the same holds for any finite product of these domains. Thus the unit balls of JB-triples are natural generalizations of the unit disc in C and we have a setting in which a large number of bounded symmetric homogeneous domains may be studied simultaneously.

Keywords

JB-triple
Linearly invariant family
Trace-order

Cited by (0)