Infinite dimensional holomorphic homogeneous regular domains

TL;DR

This paper extends the concept of holomorphic homogeneous regular domains to infinite dimensions, characterizes bounded symmetric cases, and analyzes the squeezing function, revealing new properties of infinite dimensional complex domains.

Contribution

It generalizes finite dimensional HHR domains to infinite dimensions and characterizes bounded symmetric HHR domains, including exceptional cases.

Findings

Infinite dimensional HHR domains are domains of holomorphy.

Complete classification of infinite dimensional bounded symmetric HHR domains.

Computed the greatest lower bound of the squeezing function for HHR bounded symmetric domains.

Abstract

We extend the concept of a finite dimensional {\it holomorphic homogeneous regular} (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of holomorphy and determine completely the class of infinite dimensional bounded symmetric domains which are HHR. We compute the greatest lower bound of the squeezing function of all HHR bounded symmetric domains, including the two exceptional domains. We also show that uniformly elliptic domains in Hilbert spaces are HHR.