Spectral gaps of Schrödinger operators and diffusion operators on abstract Wiener spaces

In this paper we extend the spectral gap comparison theorem of Andrews and Clutterbuck (2011) [2] to the infinite dimensional setting. More precisely, we prove that the spectral gap of Schrödinger operator −L⁎+V (L⁎ is the Ornstein-Uhlenbeck operator) on an abstract Wiener space is greater than that of the one-dimensional operator −d2ds2+sdds+V˜(s), provided that V˜ is a modulus of convexity for V. Similar result is established for the diffusion operator −L⁎+∇F⋅∇.