A Correction to the Paper 'Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups'

It is asserted in Definition 4.2 in [1] that the random operators U ( t ) defined there are unitary. As was pointed out to the author by Shizan Fang, it is clear that U ( t ) is an isometry but it is not obvious that U ( t ) is surjective. The purpose of this note is to fill this gap.