Separating Vector Bundle Sections by Invariant Means
  We sharpen the construction of representation space in the paper "Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations". We show that the principal series representation spaces constructed there, are completions of spaces of sections of Hilbert bundles rather than completions of quotient spaces of sections. 
Gestur Olafsson and Joseph A. Wolf
math.RT math.DG math.GR