Infinite Dimensional Holomorphic Homogeneous Regular Domains

Abstract

We extend the concept of a finite dimensional 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.

Correction to: Infinite Dimensional Holomorphic Homogeneous Regular Domains

“…There is a gap in the proof of the last assertion of Lemma 2.3 in the paper [2] which appeared in Volume 30 of this journal. The arguments given there are only valid in finite dimensions since the boundary ∂ need not be weakly closed in infinite dimension.…”