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 operatorsU(t) defined there are unitary. As was pointed out to the author by Shizan Fang, it is clear thatU(t) is an isometry but it is not obvious thatU(t) is surjective. The purpose of this note is to fill this gap.